Find the polar equation of the conic with the focus at the pole, directrix x = -5, and eccentricity 2.

Given:

Directrix x = -5 and eccentricity = 2

To find:

The polar equation of the conic.

Solution:

Eccentricity = 2 > 0

Therefore the conic must be a hyperbola.

Directrix is vertical (at x = -5) and the vertical directrix is located to the left of the pole.

So that the equation is of the form:

Since the eccentricity of this hyperbola is 1

The distance between the pole and directrix is

p = |-5|= 5

Substitute these in the above equation.

The polar equation of the conic is hyperbola.

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