Question

Derive the standard form of the parabola

Answer 1

Parabola is defined as distance of each point on it is equidistant from a fixed line,point.

Consider Line $x=-a,point(a,0)$

Let $(x,y)$ be any ordinary point on parabola

$|x+a|=\sqrt{{(x-a)}^2+{(y-0)}^2}$

${|x+a|}^2={(x-a)}^2+{(y-0)}^2$

$y^2={(x+a)}^2-{(x-a)}^2$

Hence $y^2=4ax$

So $y^2=4ax$ is standard form of the parabola