Question

27. Find a polar equation of the conic with focus at the pole that has the given eccentricity and equation of directrix.
e=\frac{4}{3}, r \cos \theta=-3

Answer 1

The polar equation will be  $r=\dfrac{4}{1+cos\theta}$

What is the polar equation?

A polar equation is any equation that expresses the relationship between r and theta, where r is the distance between the pole (origin) and a point on a curve, and theta is the counterclockwise angle formed by a point on a curve, the pole, and the positive x-axis.

From the equation, we are told that

The  Eccentricity: e = 1

The  Directrix is   y = 4

Generally, the polar equation for e =  1  and y  =  + c is mathematically represented as

$r =\dfrac{e\times c}{1+ecos\theta}$

$r =\dfrac{1\times 4}{1+1\times cos\theta}$  

 $r=\dfrac{4}{1+cos\theta}$

 

Therefore the polar equation will be  $r=\dfrac{4}{1+cos\theta}$

To know more about the polar equation follow

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