Question

Find a polar equation r for the conic with its focus at the pole and the given eccentricity and directrix. (For convenience, the equation for the directrix is given in rectangular form.)

Conic: Parabola Eccentricity: e = 1 Directrix: y = 4

Answer 1

The equation is
`r = (4 )/( 1 + cos (\theta ))`

Explanation:

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 = (e * c )/( 1 + ecos (\theta ))`

So

`r = (1 * 4 )/( 1 + 1 * cos (\theta ))`

`r = (4 )/( 1 + cos (\theta ))`