Worksheet: Polar Equation of a Conic

In this worksheet, we will practice determining the type of a conic section (ellipse, parabola, or hyperbola) and finding the equation of its directrix using polar equations of conics.

Q1:

Consider the polar equation 𝑟 = 𝑒 𝑑 1 + 𝑒 ( 𝜃 ) c o s of a conic with its focus at the pole and eccentricity 𝑒 , where 𝑒 > 0 and 𝑑 > 0 .

State the equation of the directrix.

  • A 𝑦 = 𝑑
  • B 𝑥 = 𝑑
  • C 𝑦 = 𝑑
  • D 𝑥 = 𝑑
  • E 𝑥 = 𝑒 𝑑

Q2:

Consider the following polar equation of a conic: 𝑟 = 6 1 2 ( 𝜃 ) c o s .

Determine the value of the eccentricity.

State the type of conic that is described by the equation.

  • ACircle
  • BEllipse
  • CParabola
  • DHyperbola

Which of the following is a directrix of the conic?

  • A 𝑥 = 2
  • B 𝑥 = 3
  • C 𝑥 = 3
  • D 𝑦 = 3
  • E 𝑦 = 3

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