Question

Find the equation of the parabola whose focus is $(1,-1)$ and whose vertex is $(2,1).$ also find its axis and latus rectum.

Answer 1

given ,

The Focus of Parabola $(1,-1)$

The vertex of Parabola is $(2,1)$

The Distance between Focus and vertex $\left(a\right)=\sqrt{(2-1{)}^2+(1+1{)}^2}\sqrt{1+4}\sqrt{5}$

The equation of parabola is $(y-1{)}^2=4\sqrt{5}(x-2)y^2-2y+1=4\sqrt{5}x-8\sqrt{5}$