Question

Ends of latus rectum of a parabola are $-3,1$ and $1,1$, then one of the equation of the parabola is

Answer 1

Mid point of Latus Rectum gives Focus of Parabola which is$(-2,1)$

Lentgh of latus rectum is $4a⟹a=1$

Slope of latus rectum is $\frac{1-1}{1+3}=0$

Axis is perpendicular to latus rectum so Slope of Axis is $\infty$ i.e., parallel to $Y-axis$ and passes through $(-2,1)$

So equation of Axis is $x=-2$

Vertices are $(2,0)$ or $(2,2)$

considering $(2,0)$

General form of equation is $(x-h{)}^2=4a(y-k)$

$⟹(x-2{)}^2=4(1\left)\right(y)$

$⟹x^2-2x+4=4y$