Standard Form of the Equation

Key Questions

• What is the standard form of the equation of a hyperbola?

  Answer:

  #(x-h)^2/a^2-(y-k)^2/b^2=1#

  Explanation:

  

  mason m · 1 · Dec 17 2015
• Why is a hyperbola considered a conic section?

  Conic sections are the intersections of a plane and a cone.

  When you cut the cone with a plane that is parallel to the base of the cone, you end up with a circle.

  When you cut the cone with a plane that is not parallel to the base of the cone and the plane does not cut through the base, you end up with an ellipse. If the plane cuts through the base, you end up with a parabola.

  In the case of the hyperbola, you need 2 cones with their bases parallel and away from each other. When your plane cuts through both cones, you have a hyperbola.

  seph · 1 · Nov 2 2014
• How can I tell the equation of a hyperbola from the equation of an ellipse?

  When both #X^2# and #Y^2# are on the same side of the equation and they have the same signs, then the equation is that of an ellipse. If the signs are different, the equation is that of a hyperbola

  Example:

  #X^2/4 + Y^2/9 = 1#
  #9X^2 + 4Y^2 = 36#

  For both cases, X and Y are positive. Hence Ellipse.

  #X^2/4 - Y^2/9 = 1#
  #9Y^2 - 4X^2 = 36#

  For these cases, X and Y have different signs. Hence hyperbola

  seph · 1 · Oct 7 2014

• What is the standard form of the equation of a hyperbola?
• What conic section is represented by the equation #(y-2)^2/16-x^2/4=1#?
• What conic section is represented by the equation #y^2/9-x^2/16=1#?
• What conic section is represented by the equation #x^2/9-y^2/4=1#?
• How can I tell the equation of a hyperbola from the equation of an ellipse?
• What does the equation #9y^2-4x^2=36# tell me about its hyperbola?
• What does the equation #(x+2)^2/4-(y+1)^2/16=1# tell me about its hyperbola?
• What does the equation #(x-1)^2/4-(y+2)^2/9=1# tell me about its hyperbola?
• Why is a hyperbola considered a conic section?
• How do you write the equation of a hyperbola in standard form given Foci: (3,+-2) and Asymptotes: y = +-2(x-3)?
• How do you classify #13x² + 13y² - 26x + 52y = -78#?
• What is the difference between identifying a parabola, ellipse, hyperbola, and a circle?
• How do you write an equation of a hyperbola given the foci of the hyperbola are (8 , 0) and (−8 , 0), and the asymptotes are y =sqrt(7)x and y =−sqrt(7)x?
• How do you find an equation of the hyperbola with its center at the origin. Vertices (+OR- 3,0); Foci: (+OR- 5,0)?
• How do you find an equation of the hyperbola given Vertices: (2,3), (2,-3); Foci: (2,5), (2,-5)?
• How do you find an equation of hyperbola with given foci and asymptote: Foci: (0,0) and (0,4) Asymptote: y= +/-[(1/2)]x + 2?
• How do you find an equation of hyperbola with given endpoints of the transverse axis: (0,-6),(0,6); Asymptote: y=3/10 x?
• What does hyperbola mean in math?
• What are hyperbolas used for in real life?
• How do you find the standard form of the hyperbola that satisfies the given conditions: Vertices at #(0, +-2)#, foci at #(0, +-4)#?
• What are the critical points of #x^2/9 + y^2/36 = 1#?
• How do you write the equation of the ellipse #9x^2 + 4y^2 – 72x + 40y + 208 = 0#in standard form?
• How do you graph the ellipse #36x^2 + 9y^2 = 324#?
• How do you determine circle, parabola, ellipse, or hyperbola from equation #4x^2 + 9y^2 - 16x +18y -11 = 0#?
• How do you determine circle, parabola, ellipse, or hyperbola from equation #4x^2 - 9y^2 - 16x +18y -11 = 0#?
• How do you determine circle, parabola, ellipse, or hyperbola from equation #x^2 + y^2 - 16x + 18y - 11 = 0#?
• How do you identify the critical points for #(x-1)^2 = (y+1)^2#?
• How do you identify the type of conic #4x^2+8y^2-8x-24=4# is, if any and if the equation does represent a conic, state its vertex or center?
• How do you identify the following equation #(x-1)^2/9 - (y+2)^2/25 = 1# as a circle, parabola, ellipse or hyperbola?
• How do you identify the following equation # 9x^2 - 3y^2 = 27# as a circle, parabola, ellipse or hyperbola?
• How do you identify the following equation #x = (y + 4)^2 - 2# as a circle, parabola, ellipse or hyperbola?
• How do you identify the following equation #y = (x-1)^2 + 3# as a circle, parabola, ellipse or hyperbola?
• How do you identify the following equation #(x - 1)^2 + y^2/25 = 1# as a circle, parabola, ellipse or hyperbola?
• How do you find the standard form given vertices (-6, -2) and (6,-2) and foci of (-8, -2) and (8, -2)?
• How do you write an equation for the hyperbola with a centre at (-3,1), one focus (-5,1), length of conjugate axis 4?
• How do you write an equation for the hyperbola with vertices (0,2) and (0,-2) and foci at (0,9) and (0,-9)?
• How do you write an equation for the hyperbola with asymptote #y=+-(4x)/3#, contains #(3sqrt(2,)4)#?
• How do you write an equation for the hyperbola with focus at (0, 25), asymptotes intersecting at (0, 5) and an asymptote passing through (24, 13)?
• How do you write an equation for the hyperbola with center at (-2,-3), Focus at (-4,-3), Vertex at (-3,-3)?
• How do you write an equation for the hyperbola with center (0,0), vertex (-2,0) and focus (4,0)?
• How do you write an equation for the hyperbola with Foci: #(0,0)# and #(0,4)# Asmyptotes: #y= +-1/2x + 2#?
• How do you write an equation for the hyperbola with foci is at (2,2) and (6,2). and the asymptotes are y=x-2 and y=6-x?
• How do you write a standard form equation for the hyperbola with #9x^2-100y^2+18x+600y+9=0#?
• How do you write a standard form equation for the hyperbola with #9x^2 – y^2 – 36x + 4y + 23 = 0#?
• How do you write a standard form equation for the hyperbola with #36x^2 - 100y^2 - 72x + 400y = 3964#?
• How do you write a standard form equation for the hyperbola with asymptotes are at y= 1/2 x and y= -1/2x. The hyperbolas vertices are at (-3,0) and (3,0)?
• How do you write a standard form equation for the hyperbola with #y^2 - 4y - 4x^2 + 8x = 4#?
• How do you write a standard form equation for the hyperbola with vertices at (-2, 0) and (2, 0) and foci at (-6, 0) and (6, 0)?
• How do you write a standard form equation for the hyperbola with foci at (3,11) and (3,-5) and vertices at (3,7) and (3,-1)?
• How do you write a standard form equation for the hyperbola with foci are (-6,0) and (6,0) and the difference of the focal radii is 10?
• How do you write a standard form equation for the hyperbola with # y^2+2y-2x+5=0#?
• How do you write a standard form equation for the hyperbola with Vertices at #(1, -3)# and #(1,1)#; asymptote the line #y + 1 = (3/2)(x - 1)#?
• How do you write the hyperbola #36x^2-9y^2=324# in standard form?
• How do you write the hyperbola #36x^2-9y^2=324# in standard form?
• How do you write the hyperbola #36y^2-4x^2=9# in standard form?
• How do you write the hyperbola #16y^2-36x^2+9=0# in standard form?
• How do you write the hyperbola #y^2-x^2/36=4# in standard form?
• How do you write the hyperbola #x^2/9-4y^2/9=9# in standard form?
• How do you write the standard form of the hyperbola #-x^2+y^2-18x-14y-132=0#?
• How do you write the standard form of the hyperbola #9x^2-4y^2-90x+32y-163=0#?
• How do you write the standard form of the hyperbola #-16x^2+9y^2+32x+144y-16=0#?
• How do you write the standard form of the hyperbola #-2x^2+3y^2+4x-60y+268=0#?
• How do you write the equation for a hyperbola given vertices (-5,0) and (5,0), conjugate axis of lengths 12 units?
• How do you write the equation for a hyperbola given vertices (0,-4) and (0,4), conjugate axis of lengths 14 units?
• How do you write the equation for a hyperbola given vertices (9,-3) and (-5,-3), foci #(2+-sqrt53,-3)#?
• How do you find the equation for a hyperbola centered at the origin with a horizontal transverse axis of lengths 8 units and a conjugate axis of lengths 6 units?
• How do you find the equation for a hyperbola centered at the origin with a vertical transverse axis of lengths 12 units and a conjugate axis of length 4 units?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #x^2/81-y^2/49=1#?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #y^2/36-x^2/4=1#?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #y^2/16-x^2/25=1#?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #x^2/9-y^2/25=1#?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #x^2-2y^2=2#?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #x^2-y^2=4#?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #y^2=36+4x^2#?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #(y-4)^2/16-(x+2)^2/9=1#?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #(y-3)^2/25-(x-2)^2/16=1#?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #(x+1)^2/4-(y+3)^2/9=1#?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #(x+6)^2/36-(y+3)^2/9=1#?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #y^2-3x^2+6y+6x-18=0#?
• How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #4x^2-25y^2-8x-96=0#?
• For f(x, y)=x-y, how do you prove that the equation #f(x, y)= x f(y,x)# represents a hyperbola? find its asymptotes?
• How do you find the standard form of the equation of the hyperbola given the properties vertex (0,1), vertex (8,1), focus (-3,1)?
• How do you find the standard form of the equation of the hyperbola given the properties foci #(+-5,0)#, length of the conjugate axis 6?
• How do you find the standard form of the equation of the hyperbola given the properties vertices (3,2), (13,2); endpoints of the conjugate axis (8,4), (8,0)?
• How do you find the standard form of the equation of the hyperbola given the properties vertices (-10,5), asymptotes #y=+-1/2(x-6)+5#?
• How do you find the standard form given #x^2-2x-4y-11=0#?
• How do you find the standard form given #x^2+y^2-8x+4y+11=0#?
• How do you find the standard form given #9x^2+4y^2-36x+24y+36=0#?
• How do you find the standard form given #9x^2-4y^2-36x-24y-36=0#?
• How do you find the standard form given #y^2+8y-4x+16=0#?
• How do you find the standard form given #4x^2+y^2-8x+4=0#?
• How do you find the standard form given #4x^2+9y^2-8x+54y+49=0#?
• How do you find the standard form given #x^2+y^2-6x+4y+14=0#?
• How do you find the standard form given #2x^2+4y^2+12x-8y+25=0#?
• How do you find the standard form given #4x^2-5y^2-40x-20y+160=0#?