Question

Find the equation of parabola whose focus is $S(1,-7)$ and vertex is $A(1,-2)$.

Answer 1

Since focus is $(1,-7)$ and $(1,-2)$

So axis of the parabola is parallel to y-axis

So equation of parabola can be given by, $(x-1{)}^2=-4a(y+2)$,

since vertex is $(1,-2)$ and focus is below vertex

Now $a$ distance between focus and vertex $=5$

Hence the required parabola is $(x-1{)}^2=-20(y+2)$