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.

Q1:

A conic with focus at the pole has eccentricity 𝑒=12 and vertices at (0,−6) and (0,2). Write the equation of the conic in polar form.

Q2:

A conic with focus at the pole has eccentricity 𝑒=23 and directrix 𝑦=−52.

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 𝑒=32 and vertices at (−1,0) and (−5,0).

By deciding whether the directrix is in the form 𝑥=𝑑, 𝑥=−𝑑, 𝑦=𝑑, or 𝑦=−𝑑, where 𝑑>0, 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.

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