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