# 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