Question

How do I find the directrix and focus of a parabola?

Answer 1

There are two basic kinds of parabola(as it is convenient for me to say)

Type 1:
The parabola lying on, or parallel to the `x-`axis

This parabola is of the form `(y-y_v)^2=4a(x-x_v)`

Where,
- focus is `(a+x_v,y_v)`
- directrix is the line `x=x_v-a`
- Vertex is `(x_v,y_v)`

Type 2:
The parabola lying on, or parallel to the `y-`axis

This parabola is of the form `(x-x_v)^2=4a(y-y_v)`

Where,
- focus is `(x_v,a+y_v)`
- directrix is the line `y=y_v-a`
- Vertex is `(x_v,y_v)`