Write a polar equation of a conic that has its focus at the

Write a polar equation of a conic that has its focus at the origin and satifies the given conditions

ellipse, eccentricity 1/4

directrix y=-2

Solution

The polar form of an ellipse with a focus at the origin is:
r =e*d/(1 +/ - ecos )

It would be + as directrix is parallel to x axis:

r =e*d/(1 +ecos )

e = 0.25

directrix : y= -2. So d= 2

So, plugging these values in the formula above:

r = 0.25*2/(1 +0.25cos)

r = 0.5/( 1+ 0.25cos) ----> Polar equation of ellipse