Question

What is the focus and directrix of a parabola?

Answer 1

Focus and directrix of a parabola:

A parabola is the locus of a point that is equidistant from a fixed point and a fixed-line.

The fixed point is called the focus and the fixed line is called a directrix.

The standard form of a vertical parabola is ${\left(x-h\right)}^2=4p\left(y-k\right)$.

The directrix of the parabola is $y=k-p$.

The focus of the parabola is $\left(h,k+p\right)$.

The standard form of a vertical parabola is ${\left(y-k\right)}^2=4p\left(x-h\right)$.

The directrix of the parabola is $x=h-p$.

The focus of the parabola is $\left(h+p,k\right)$.