# Worksheet: Polar Equation of a Conic

In this worksheet, we will practice determining the type of a conic section (ellipse, parabola, or hyperbola) and writing polar equations of conics given the eccentricity and some other characteristic.

**Q1: **

A conic with focus at the pole has eccentricity and vertices at and . Write the equation of the conic in polar form.

- A
- B
- C
- D
- E

**Q2: **

A conic with focus at the pole has eccentricity and directrix .

Identify the type of the conic.

- AEllipse
- BHyperbola
- CParabola
- DCircle

Write the equation of the conic in polar form.

- A
- B
- C
- D

**Q3: **

A conic with its focus at the pole has eccentricity and vertices at and .

Identify the type of the conic.

- ACircle
- BEllipse
- CHyperbola
- DParabola

By deciding whether the directrix is in the form , , , or , where , select the form of the polar equation of the conic.

- A
- B
- C
- D

By writing one of the vertices in polar form, find the equation of the directrix.

- A
- B0
- C
- D

Hence, write the equation of the conic.

- A
- B
- C
- D

**Q4: **

Consider the polar equation of a conic with its focus at the pole and eccentricity , where and .

State the equation of the directrix.

- A
- B
- C
- D
- E

**Q5: **

Consider the following polar equation of a conic: .

Determine the value of the eccentricity.

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

- AEllipse
- BParabola
- CHyperbola
- DCircle

Which of the following is a directrix of the conic?

- A
- B
- C
- D
- E