Question

Find the equation of the parabola with latus - rectum joining points $(4,6)$ and $(4,-2)$

Answer 1

Latus-rectum joining points are $(4,6)$ and $(4,-2)$.
Length of latus-rectum $=4a$
$\Rightarrow \sqrt{(4-4{)}^2+(6+2{)}^2}=4a$
$\Rightarrow \sqrt{(8{)}^2}=4a$
$\therefore 4a=8$
Hence equation of parabola
$Y^2=4ax$
$Y^2=8x$
$\therefore (y-2{)}^2=8x$