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

1 Answer
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 #(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)#