Lesson: Polar Equation of a Conic Mathematics • 12th Grade

In this lesson, we will learn how to determine the type of a conic section (ellipse, parabola, or hyperbola) and write polar equations of conics given the eccentricity and some other characteristic.

Lesson Plan

Students will be able to

identify information about a conic section from its polar equation,
write the polar equation of a conic section from
- its equation in rectangular form,
- its properties,
- its graph,
solve real-world problems using the polar equation of a conic section.

Lesson Worksheet

Q1:

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

Q2:

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

Identify the type of the conic.

Write the equation of the conic in polar form.

Q3:

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

Identify the type of the conic.

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

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

Hence, write the equation of the conic.