Question

Find the equation of the parabola the extremities of whose latus rectum are $(1,2)$ and $(1,-4)$.

Answer 1

Let $A$ and $B$ be the endpoint of latus rectum of given parabole

respectively.

$\Rightarrow AB=6$ unit

We know focuses is midpoint of latus rectum.Then coordinates of focus $s=(1,-1)$

$\Rightarrow y=-1$ is axis of parabola and $x=-2$ is tangent at vertex.

$\Rightarrow$ Equation of parabola $\Rightarrow \left[\right(y-(-1){)}^2=4\times a(x-(-2\left)\right)]$

$=(y+1{)}^2=4\times 3(x+2)$

$=(y+1{)}^2=12(x+2)$