Question

The following equation is a conic section written in polar coordinates.=51 + 5sin(0)Step 2 of 2: Find the equation for the directrix of the conic section.

Answer 1

For a conic with a focus at the origin, if the directrix is

`y=\pm p`

where p is a positive real number, and the eccentricity is a positive real number e, the conic has a polar equation

`r=(ep)/(1\pm e\sin\theta)`

if 0 ≤ e < 1 , the conic is an ellipse.

if e = 1 , the conic is a parabola.

if e > 1 , the conic is an hyperbola.

In our problem, our equation is

`r=(5)/(1+5\sin\theta)`

If we compare our equation with the form presented, we have

`\begin{cases}e={5} \\ p={1}\end{cases}`

Therefore, the directrix is

`y=1`