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

Apr 18, 2015

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 ${\left(y - {y}_{v}\right)}^{2} = 4 a \left(x - {x}_{v}\right)$

Where,
- focus is $\left(a + {x}_{v} , {y}_{v}\right)$
- directrix is the line $x = {x}_{v} - a$
- Vertex is $\left({x}_{v} , {y}_{v}\right)$

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

This parabola is of the form ${\left(x - {x}_{v}\right)}^{2} = 4 a \left(y - {y}_{v}\right)$

Where,
- focus is $\left({x}_{v} , a + {y}_{v}\right)$
- directrix is the line $y = {y}_{v} - a$
- Vertex is $\left({x}_{v} , {y}_{v}\right)$