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Worksheet: Polar Equation of a Conic

Q1:

Consider the polar equation π‘Ÿ = 𝑒 𝑑 1 + 𝑒 ( πœƒ ) 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 π‘₯ = βˆ’ 𝑑
  • C 𝑦 = βˆ’ 𝑑
  • D π‘₯ = 𝑑
  • E π‘₯ = 𝑒 𝑑

Q2:

Consider the following polar equation of a conic: π‘Ÿ = 6 1 βˆ’ 2 ( πœƒ ) 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 π‘₯ = βˆ’ 2
  • B π‘₯ = 3
  • C π‘₯ = βˆ’ 3
  • D 𝑦 = βˆ’ 3
  • E 𝑦 = 3