Polar Coordinates

Key Questions

• How do you find the polar coordinates of the point?

  Answer:

  I am assuming that you want to convert a point in Cartesian Coordinate form to Polar Coordinate Form.

  I will use an example in the explanation below.

  Explanation:

  Let us say that we want to convert a point #(0, 2)# in Cartesian Form to Polar Form.

  Let us analyze the image below:

  

  We have a right-triangle and hence we can use Pythagoras Theorem to define a relationship:

  #x^2 + y^2 = r^2#

  #tan theta = y/x#

  We can see that

  #cos theta = x/r#

  Hence,

  #color(blue)(x=r cos theta# #color(red)([ 1 ]#

  #sin theta = y/r#

  Hence,

  #color(blue)(y = r sin theta# #color(red)([ 2 ]#

  Observe that, if we are given the point #(x, y)#, then we can define #(r, theta)# and express #(x,y)# in terms of #(r cos theta, r sin theta)#.

  Now, let us work on the point in Cartesian coordinate form, in our example:

  #(0,2)#

  Let us plot this point and look at the graph:

  

  Now, we are in a position to convert the #(0, 2)# to equivalent Polar form using #color(red)([ 1 ]# and #color(red)([ 2 ]#

  Polar form is #color(green)((r, theta)#

  #rArr color(blue)((2, pi/2)#

  Hope it helps.

  Sridhar V. · 1 · Mar 14 2018
• How do you find the distance between 2 polar coordinates?

  Yes! It is possible to derive formulae for both the two-dimensional and three-dimensional cases in polar coordinates. The following are the formulae:

  2-D Polar Coordinates : #\vec{r_A}=(r_A,\theta_A); \qquad \vec{r}_B=(r_B, \theta_B)#
  #S=\sqrt{|\vec{r}_B-\vec{r}_A|^2} = \sqrt{r_A^2+r_B^2-2r_Ar_B\cos(\theta_B-\theta_A)}#

  3-D Spherical Polar Coordinates :
  #\vec{r_A}=(r_A,\theta_A,\phi_A); \qquad \vec{r}_B=(r_B, \theta_B, \phi_B)#
  #S=\sqrt{|\vec{r}_B-\vec{r}_A|^2}#
  #= \sqrt{r_A^2+r_B^2-2r_Ar_B[\sin\theta_A\sin\theta_B\cos(\phi_B-\phi_A)+\cos\theta_A\cos\theta_B]}#

  Deriving these formulae requires writing the position vectors in their cartesian forms and apply the Pythagorous Theorem to find the distance between two points in space. The following trigonometric identities might be useful for this problem :

  • #\cos(A-B)=\cos(A)\cos(B)+\sin(A)\sin(B)#
  • #\sin^2A+\cos^2A=1#

  Derivation of 2-D Formula :
  #\vec{r}_A=(r_A, \theta_A) = (X_A, Y_A); \qquad \vec{r}_B=(r_B, \theta_B) = (X_B, Y_B);#
  #X_A=r_A\cos\theta_A, \quad Y_A=r_A\sin\theta_A; #
  #X_B=r_B\cos\theta_B, \quad Y_B=r_B\sin\theta_B; #

  The distance between the two points is:
  #S=\sqrt{|\vec{r}_B-\vec{r}_A|^2} = \sqrt{(X_B-X_A)^2+(Y_B-Y_A)^2}#
  #S=\sqrt{(r_B\cos\theta_B-r_A\cos\theta_A)^2+(r_B\sin\theta_B-r_A\sin\theta_A)^2}#

  Upon expanding the squares and further simplification,
  #S=\sqrt{r_A^2(\cos^2\theta_A+\sin^2\theta_A)+r_B^2(\cos^2\theta_B+\sin^2\theta_B)-2r_Ar_B(\cos\theta_A\cos\theta_B+\sin\theta_A\sin\theta_B)}#
  #S=\sqrt{r_A^2+r_B^2-2r_Ar_B\cos(\theta_B-\theta_A)}#

  Derivation of 3-D Formula :
  #\vec{r}_A=(r_A, \theta_A,\phi_A) = (X_A, Y_A,Z_A); #
  #\vec{r}_B=(r_B, \theta_B,\phi_B) = (X_B, Y_B,Z_B);#

  #X_A=r_A\sin\theta_A\cos\phi_A, \quad Y_A=r_A\sin\theta_A\sin\phi_A; Z_A=r_A\cos\theta_A#

  #X_B=r_B\sin\theta_B\cos\phi_B, \quad Y_B=r_B\sin\theta_B\sin\phi_B; Z_B=r_B\cos\theta_B#

  The distance between the two points is:
  #S=\sqrt{|\vec{r}_B-\vec{r}_A|^2} = \sqrt{(X_B-X_A)^2+(Y_B-Y_A)^2+(Z_B-Z_A)^2}#

  • #(X_B-X_A)^2 =(r_B\sin\theta_B\cos\phi_B-r_A\sin\theta_A\cos\phi_A)^2#
  • #(Y_B-Y_A)^2 =(r_B\sin\theta_B\sin\phi_B-r_A\sin\theta_A\sin\phi_A)^2#
  • #(Z_B-Z_A)^2=(r_B\cos\theta_B-r_A\cos\theta_A)^2#

  Upon expanding the squares and further simplification,

  #S=\sqrt{r_A^2(\cos^2\theta_A+\sin^2\theta_A)+r_B^2(\cos^2\theta_B+\sin^2\theta_B)-2r_Ar_B[\sin\theta_A\sin\theta_B (\cos\phi_A\cos\phi_B+\sin\phi_A\sin\phi_B)+\cos\theta_A\cos\theta_B]}#

  #=\sqrt{r_A^2+r_B^2-2r_Ar_B[\sin\theta_A\sin\theta_B \cos(\phi_B-\phi_A)+\cos\theta_A\cos\theta_B]}#

  Cosmic Defect · 2 · Dec 19 2014
• What is the difference between a rectangular coordinate system and a polar coordinate system?

  One of the most interesting differences is that every point in the plane has exactly one representation as a pair of coordinates in the rectangular (or any other parallelogram) coordinate system, but has infinitely many representations in polar coordinates.

  Example:

  The point whose rectangular coordinates are #(1,1)# corresponds to polar coordinates:
  #(sqrt2, pi/4)# and also #(sqrt2, (9 pi)/4)# and #(sqrt2, (-7 pi)/4)# and #(-sqrt2, ( 5 pi)/4)# and infinitely many others.

  Jim H · 10 · Mar 26 2015
• What does a polar coordinate system look like?

  A polar coordinate system consists of a polar axis, or a "pole", and an angle, typically #theta#. In a polar coordinate system, you go a certain distance #r# horizontally from the origin on the polar axis, and then shift that #r# an angle #theta# counterclockwise from that axis.

  This might be difficult to visualize based on words, so here is a picture (with O being the origin):

  

  This is a more detailed picture, depicting a whole polar coordinate plane (with the #theta#'s in radians):

  

  The origin is in the middle, and each circle represents a different #r# (which is actually a radius). If you follow the line of that given circle with radius #r# along the angle, you can get polar coordinate points in the form #(r,theta)#

  Note that polar coordinates/equations have Cartesian equivalents shown below:

  

  Sally · 2 · Dec 4 2014
• What are Polar Coordinates?

  Answer:

  See http://mathworld.wolfram.com/PolarCoordinates.html

  Explanation:

  I can give a simple answer, i.e. a combination of a radial coordinate r and the angle #theta#, which we give as an ordered pair #(r,theta)#.

  I believe, though, that reading up what is said other places on the Internet, for instance http://mathworld.wolfram.com/PolarCoordinates.html, will be of more help.

  Roy Ø. · 1 · May 11 2018

• What are Polar Coordinates?
• How do you find the polar coordinates of the point?
• What is the difference between a rectangular coordinate system and a polar coordinate system?
• How do you graph polar coordinates?
• What careers use polar coordinates?
• How do you plot the point #A (5, -255^\circ)# and the point #B (3, 60^\circ)#?
• What does a polar coordinate system look like?
• How do you find the distance between 2 polar coordinates?
• For the given point #A(-4, frac{pi}{4})#, how do you list three different pairs of polar coordinates that represent this point such that #-2pi \le \theta \le 2pi#?
• How do you find the rectangular form of #(4, -pi/2)#?
• What is the distance between #(4, pi/2 )# and #(2, pi/3 )#?
• What is the distance between #(4, pi/2 )# and #(2, pi/12 )#?
• What is the distance between #(4, pi/2 )# and #(5, pi/12 )#?
• What is the distance between #(4 , pi/12 )# and #(5, pi/12 )#?
• What is the distance between #(-6 , pi/2 )# and #(5, pi/12 )#?
• What is the distance between #(-6 , pi/2 )# and #(5, pi/6 )#?
• What is the distance between #(-6 , pi/2 )# and #(1 , pi/6 )#?
• What is the distance between #(-6 , pi/3 )# and #(1 , pi/6 )#?
• What is the distance between #(-6 , pi/3 )# and #(7 , pi/2 )#?
• What is the distance between #(-6 , pi/3 )# and #(7 , pi/4 )#?
• What is the distance between #(-3 , (17 pi)/12 )# and #(8 , pi/4 )#?
• What is the distance between #(-3 , (17 pi)/12 )# and #(-1 , pi/4 )#?
• What is the distance between #(-3 , (19 pi)/12 )# and #(-1 , pi/4 )#?
• What is the distance between #(-3 , (13 pi)/12 )# and #(-1 , pi/4 )#?
• What is the distance between #(-3 , (13 pi)/12 )# and #(4 , pi )#?
• What is the distance between #(-6 , (7 pi)/12 )# and #(4 , pi )#?
• What is the distance between #(-6 , (-5 pi)/12 )# and #(1 , pi )#?
• What is the distance between #(-6 , (-5 pi)/8 )# and #(1 , pi )#?
• What is the distance between #(-6 , (-13 pi)/8 )# and #(9, pi )#?
• What is the distance between #(0 , (-13 pi)/8 )# and #(9, pi )#?
• What is the distance between #(3 , (3 pi)/8 )# and #(9, pi )#?
• What is the distance between #(3 , (3 pi)/4 )# and #(9, pi )#?
• What is the distance between #(2 , (3 pi)/4 )# and #(-1 , pi )#?
• What is the distance between #(12 , (-3 pi)/4 )# and #(-1 , pi )#?
• What is the distance between #(5 , (7 pi)/4 )# and #(-4 , pi )#?
• What is the distance between #(2 , (7 pi)/4 )# and #(8 , (3 pi )/2 )#?
• What is the distance between #(2 , (5 pi)/4 )# and #(8 , (3 pi )/2 )#?
• What is the distance between #(2 , (5 pi)/4 )# and #(8 , (2 pi )/3 )#?
• What is the distance between #(2 , (5 pi)/8 )# and #(-1 , (2 pi )/3 )#?
• What is the distance between #(2 , (5 pi)/8 )# and #(-1 , (1 pi )/3 )#?
• What is the distance between #(2 , (5 pi)/8 )# and #(3 , (1 pi )/3 )#?
• What is the distance between #(6 , (5 pi)/8 )# and #(3 , (4 pi )/3 )#?
• What is the distance between #(-6 , (5 pi)/8 )# and #(3 , (5 pi )/3 )#?
• What is the distance between #(3 ,(5 pi)/6 )# and #(-2 , (5 pi )/12 )#?
• What is the distance between #(3 ,(7 pi)/6 )# and #(-2 , (5 pi )/12 )#?
• What is the distance between #(2 ,(7 pi)/6 )# and #(2 , (5 pi )/12 )#?
• What is the distance between #(2 ,(7 pi)/6 )# and #(2 , (23 pi )/12 )#?
• What is the distance between #(2 ,(5 pi)/6 )# and #(4 , (23 pi )/12 )#?
• What is the distance between #(2 ,(5 pi)/6 )# and #(-1 , (23 pi )/12 )#?
• What is the distance between #(2 ,(5 pi)/6 )# and #(-1 , (19 pi )/12 )#?
• What is the distance between #(4 ,(5 pi)/6 )# and #(-1 , (19 pi )/12 )#?
• What is the distance between #(-3 ,(5 pi)/6 )# and #(-1 , (11 pi )/12 )#?
• What is the distance between #(-3 ,(5 pi)/6 )# and #(5 , (11 pi )/12 )#?
• What is the distance between #(-3 ,(5 pi)/6 )# and #(5 , (7 pi )/12 )#?
• What is the distance between #(2 ,(5 pi)/6 )# and #(5 , (7 pi )/12 )#?
• What is the distance between #(2 ,(5 pi)/6 )# and #(-4 , (7 pi )/4 )#?
• What is the distance between #(2 ,(7 pi)/6 )# and #(-4 , (7 pi )/4 )#?
• What is the distance between #(2 ,(7 pi)/6 )# and #(-7 , (5 pi )/4 )#?
• What is the distance between #(2 ,(7 pi)/6 )# and #(-7 , (- pi )/4 )#?
• What is the distance between #(2 ,(7 pi)/6 )# and #(3 , (- pi )/6 )#?
• What is the distance between #(2 ,(7 pi)/6 )# and #(3 , (- pi )/8 )#?
• What is the distance between #(5 ,(7 pi)/6 )# and #(3 , (- pi )/8 )#?
• What is the distance between #(5 ,(7 pi)/6 )# and #(3 , (- 7 pi )/8 )#?
• What is the distance between #(1 ,(7 pi)/6 )# and #(3 , (5 pi )/8 )#?
• What is the distance between #(1 ,(3 pi)/4 )# and #(3 , (5 pi )/8 )#?
• What is the distance between #(1 ,(3 pi)/4 )# and #(3 , (15 pi )/8 )#?
• What is the distance between #(1 ,(3 pi)/4 )# and #(2 , (15 pi )/8 )#?
• What is the distance between #(-7 ,(3 pi)/4 )# and #(2 , (15 pi )/8 )#?
• What is the distance between #(-7 ,(3 pi)/4 )# and #(2 , (13 pi )/8 )#?
• What is the distance between #(2 ,(3 pi)/4 )# and #(2 , (13 pi )/8 )#?
• What is the distance between #(2 ,(3 pi)/4 )# and #(2 , (11 pi )/8 )#?
• What is the distance between #(2 ,(7 pi)/4 )# and #(5 , (11 pi )/8 )#?
• What is the distance between #(2 ,(7 pi)/4 )# and #(5 , (11 pi )/12 )#?
• What is the distance between #(2 ,(5 pi)/4 )# and #(-2 , (11 pi )/12 )#?
• What is the distance between #(2 ,(5 pi)/4 )# and #(8 , (11 pi )/12 )#?
• What is the distance between #(5 ,(5 pi)/4 )# and #(8 , (11 pi )/12 )#?
• What is the distance between #(5 ,( pi)/4 )# and #(3 , (11 pi )/12 )#?
• What is the distance between #(5 ,( pi)/4 )# and #(3 , (11 pi )/6 )#?
• What is the distance between #(5 ,( pi)/4 )# and #(-4 , ( pi )/6 )#?
• What is the distance between #(3 ,( pi)/4 )# and #(-2 , ( pi )/6 )#?
• What is the distance between #(3 ,( pi)/4 )# and #(-2 , ( pi )/2 )#?
• What is the distance between #(3 ,( pi)/4 )# and #(4 , ( pi )/2 )#?
• What is the distance between #(1 ,( pi)/4 )# and #(4 , ( pi )/2 )#?
• What is the distance between #(1 ,( pi)/4 )# and #(4 , ( 3 pi )/2 )#?
• What is the distance between #(1 ,( pi)/4 )# and #(-1 , ( 3 pi )/2 )#?
• What is the distance between #(1 ,( pi)/4 )# and #(-4 , ( 3 pi )/2 )#?
• What is the distance between #(3 ,( pi)/12 )# and #(-4 , ( 3 pi )/2 )#?
• What is the distance between #(3 ,( pi)/12 )# and #(-2 , ( 3 pi )/2 )#?
• What is the distance between #(3 ,( 5 pi)/12 )# and #(-2 , ( 3 pi )/2 )#?
• What is the distance between #(3 ,( 5 pi)/12 )# and #(-2 , ( pi )/2 )#?
• What is the distance between #(-5 ,( 5 pi)/12 )# and #(-2 , ( pi )/2 )#?
• What is the distance between #(-5 ,( 5 pi)/12 )# and #(3 , ( pi )/2 )#?
• What is the distance between #(-5 ,( 5 pi)/6 )# and #(3 , ( pi )/2 )#?
• What is the distance between #(-5 ,( 5 pi)/6 )# and #(1 , ( pi )/2 )#?
• What is the distance between #(4 ,( 5 pi)/6 )# and #(1 , ( -3 pi )/2 )#?
• What is the distance between #(4 ,( 7 pi)/6 )# and #(3 , ( -3 pi )/2 )#?
• What is the distance between #(4 ,( 7 pi)/6 )# and #(3 , ( - pi )/2 )#?
• What is the distance between #(4 ,( 7 pi)/6 )# and #(-1 ,( 3pi )/2 )#?
• What is the distance between #(4 ,( 7 pi)/8 )# and #(-1 ,( 3pi )/2 )#?
• What is the distance between #(4 ,( 9 pi)/8 )# and #(-4 ,( 3pi )/2 )#?
• What is the distance between #(4 ,( 9 pi)/8 )# and #(-1 ,( 3 pi )/2 )#?
• What is the distance between #(4 ,( -3 pi)/8 )# and #(-1 ,( 3 pi )/2 )#?
• What is the distance between #(4 ,( - pi)/8 )# and #(-1 ,( 3 pi )/2 )#?
• What is the distance between #(4 ,( - 3pi)/8 )# and #(-1 ,( 3 pi )/4 )#?
• What is the distance between #(4 ,( - 3pi)/8 )# and #(7 ,( 3 pi )/4 )#?
• What is the distance between #(4 ,( - 3pi)/4 )# and #(7 ,( 3 pi )/4 )#?
• What is the distance between #(4 ,( - 3pi)/4 )# and #(2 ,( 3 pi )/4 )#?
• What is the distance between #(4 ,( - 3pi)/4 )# and #(-2 ,( pi )/4 )#?
• What is the distance between #(3 ,( - 3pi)/4 )# and #(-2 ,( 7 pi )/4 )#?
• What is the distance between #(-9 ,( - 3pi)/4 )# and #(-2 ,( 5 pi )/4 )#?
• What is the distance between #(-9 ,( 17 )/12 )# and #(-2 ,( 5 pi )/4 )#?
• What is the distance between #(-9 ,( 17 )/12 )# and #(-2 ,(-7 pi )/4 )#?
• What is the distance the polar coordinates #(-2 ,( -3 )/8 )# and #(4 ,(-7 pi )/4 )#?
• What is the distance the polar coordinates #(-2 ,( -3 )/8 )# and #(6 ,(-7 pi )/4 )#?
• How do you plot the polar coordinate #(2, (-11pi)/6)#?
• How do you plot the polar coordinate #(2, (7pi)/6)#?
• How do you plot the polar coordinate #(2, (5pi)/6)#?
• How do you plot the polar coordinate #(-2, (7pi)/6)#?
• How do you plot the polar coordinate #(2, (11pi)/6)#?
• How do you plot the polar coordinate #(3, 90^o)#?
• How do you plot the polar coordinate #(4,135^o)#?
• How do you plot the polar coordinate #(-2,120^o)#?
• How do you plot the polar coordinate #(-3, (3pi)/4)#?
• How do you plot the polar coordinate #(4, (-4pi)/3)#?
• How do you plot the polar coordinate #(-2, -45^o)#?
• How do you plot the polar coordinate #(-3, (-pi)/3)#?
• How do you find the rectangular coordinates given #(3, pi/2)#?
• How do you find the rectangular coordinates given #(-2, 0)#?
• How do you find the rectangular coordinates given #(6, 150^o)#?
• How do you find the polar coordinates given #(-2,2)#?
• How do you find the polar coordinates given #(1,-1)#?
• How do you find the polar coordinates given #(sqrt3, 1)#?
• How do you find the polar coordinates given #(-2, -2sqrt3)#?
• How do you change the polar coordinate #(4,45^o)# into rectangular coordinates?
• How do you change the polar coordinate #(-6, pi)# into rectangular coordinates?
• How do you change the polar coordinate #(9, -pi/3)# into rectangular coordinates?
• How do you change the rectangular coordinate #(-6, 6sqrt3)# into polar coordinates?
• How do you plot the polar coordinate #(3,150^o)#?
• How do you plot the polar coordinate #(3,(11pi)/6)#?
• How do you plot the polar coordinate #(-3,(23pi)/12)#?
• How do you plot #A(4,0^o)#, #B(7,180^o)#, and #C(9,45^o)# in a polar coordinate system?
• How do you plot #A(-6,-pi/6)#, #B(-5,-pi/2)#, and #C(-8,-pi/4)# in a polar coordinate system?
• How do you convert the polar coordinate #(6,pi/6)# into rectangular coordinates?
• How do you convert the polar coordinate #(7,(2pi)/3)# into rectangular coordinates?
• How do you convert the polar coordinate #(-2,(7pi)/8)# into rectangular coordinates?
• How do you convert the polar coordinate #(3,-(3pi)/7)# into rectangular coordinates?
• How do you convert the polar coordinate #(-9.028 , -0.663)# into rectangular coordinates?
• How do you convert the rectangular coordinate #(-8,0)# into polar coordinates?
• How do you convert the rectangular coordinate #(0,-5)# into polar coordinates?
• How do you convert the rectangular coordinate #(-5,-5)# into polar coordinates?
• How do you convert the rectangular coordinate #(1,-sqrt3)# into polar coordinates?
• How do you convert the rectangular coordinate #(9.79, 5.13)# into polar coordinates?
• How do you convert the rectangular coordinate #(-4.26,31.1)# into polar coordinates?
• How do you plot the point #(5,60^o)# on a polar graph?
• How do you plot the point #(5,-60^o)# on a polar graph?
• How do you plot the point #(-5,60^o)# on a polar graph?
• How do you plot the point #(-5,-60^o)# on a polar graph?
• How do you plot the point #(-3,-150^o)# on a polar graph?
• How do you convert the rectangular point #(3,3)# into polar form?
• How do you convert the rectangular point #(2,2sqrt3)# into polar form?
• How do you convert the rectangular point #(0,-2)# into polar form?
• How do you convert the polar coordinate point #(-2,pi)# into rectangular form?
• How do you convert the polar coordinate point #(3,135^o)# into rectangular form?
• How do you convert the polar coordinate point #(-5,240^o)# into rectangular form?
• How do you graph the point #A(1,135^o)#?
• How do you graph the point #B(2.5, -pi/6)#?
• How do you graph the point #C(-3,-120^o)#?
• How do you graph the point #D(-2,(13pi)/6)#?
• How do you find the distance between #P_1(2.5,pi/6)# and #P_2(-3,-pi/4)# on the polar plane?
• How do you graph the point #E(2,30^o)#?
• How do you graph the point #L(3,-pi/6)#?
• How do you graph the point #M(2,-90^o)#?
• How do you graph the point #N(-1,120^o)#?
• How do you graph the point #P(-0.5, -(11pi)/6)#?
• How do you graph the point #R(-7/2, 1050^o)#?
• How do you find four other pairs of polar coordinates for the point #T(1.5, 180^o)#?
• How do you find the distance between the points with the given polar coordinates #P_1(4,170^circ)# and #P_2(6,105^circ)#?
• How do you find the distance between the points with the given polar coordinates #P_1(1.3,-47^circ)# and #P_2(-3.6, -62^circ)#?
• How do you find the distance between the points with the given polar coordinates #P_1(1, pi/6)# and #P_2(5, (3pi)/4)#?
• How do you find the distance between the points with the given polar coordinates #P_1(-2.5,pi/8)# and #P_2(-1.75, -(2pi)/5)#?
• How do you find the rectangular coordinate of #(7.5,110^circ)#?
• A point in polar coordinates is given. Convert the point to rectangular coordinates? (0, −3π)
• Convert the polar equation to rectangular form? r = 3/9 cos θ − 8 sin θ
• Question #47750
• How do you convert #(6,210^circ)# from polar to cartesian coordinates?
• How do you convert #(-4, 3pi)# from polar to cartesian coordinates?
• How do you convert #(2, (11pi)/6)# from polar to cartesian coordinates?
• How do you convert #(6, 90^circ)# from polar to cartesian coordinates?
• How do you convert #(-1, 405^circ)# from polar to cartesian coordinates?
• How do you convert #(3, 1)# from cartesian to polar coordinates?
• How do you convert #(-1,-3)# from cartesian to polar coordinates?
• How do you convert #(0,2)# from cartesian to polar coordinates?
• How do you convert #(4,-2)# from cartesian to polar coordinates?
• How do you convert #(-2,0)# from cartesian to polar coordinates?
• Find the argument of #(-sqrt3 +i)^8#?
• Question #1aa2d
• Question #2bde8
• Can you help me Transform from a polar to a rectangular equation?
• What is 6y+y^2=x^2 in polar form?