Conic sections in polar coordinates

[glasshut137]

[SOLVED] conic sections in polar coordinates

Homework Statement

write a polar equation of a conic with the focus at the origin and the given data.

i know it's an ellipse with eccentricity 0.8 and vertex (1, pie/2)

The Attempt at a Solution

my question is: how do I find the directrix using the vertex and the focus point?

 

[HallsofIvy]

You can use the eccentricity, together with the distance from the focus to the vertex to determine where the center of the ellipse is. If the distance from the center to the focus is c and from the center to the vertex is a, then the distance from the center to the directrix is a²/c.