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-xaxis

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

Where,
- focus is (a+x_v,y_v)(a+xv,yv)
- directrix is the line x=x_v-ax=xva
- Vertex is (x_v,y_v)(xv,yv)

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

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

Where,
- focus is (x_v,a+y_v)(xv,a+yv)
- directrix is the line y=y_v-ay=yva
- Vertex is (x_v,y_v)(xv,yv)