Writing Polar Equations for Conic Sections

Key Questions

  • How do you identify conic sections?

    General form of the conic equation

    Ax^2+Bxy+Cy^2+Dx+Ey+F=0

    The coefficients A and C are need to identify the conic sections without having to complete the square.

    A and C cannot be 0 when making this determination.

    Parabola->A*C=0

    Circle->A=C

    Ellipse->A*C>0 and A!=C

    Hyperbola->A*C<0

    AJ Speller · · Sep 28 2014
  • What is the standard equation of a hyperbola?

    Standard form equations for the hyperbola.

    x^2/a^2-y^2/b^2=1

    The foci are located on the x-axis also called the transverse .

    y^2/a^2-x^2/b^2=1

    The foci are located on the y-axis also called the transverse .

    AJ Speller · · Sep 28 2014
  • What is the standard equation of a parabola?

    Standard form for the equation of a parabola is the same as standard for for a quadratic function:
    y =ax^2+bx+c

    Or
    f(x) = ax^2+bx+c.

    For graphing, many prefer the vertex form

    y=a (x-h)^2 +k

    Jim H · 1 · Apr 25 2015
  • What is the meaning of conic section?

    Answer:

    A conic section is a section (or slice) through a cone.

    Explanation:

    Depending on the angle of the slice, you can create different conic sections,

    Conic Sections
    (from en.wikipedia.org)

    If the slice is parallel to the base of the cone, you get a circle.

    If the slice is at an angle to the base of the cone, you get an ellipse.

    If the slice is parallel to the side of the cone, you get a parabola.

    If the slice intersects both halves of the cone, you get a hyperbola.

    There are equations for each of these conic sections, but we will not include them here.

    Ernest Z. · 2 · Sep 15 2015

Questions

Polar Equations of Conic Sections