Question

The area of the triangle formed by the lines joining the vertex of the parabola, $x^2=8y$ to the extremities of its latus rectum is :

• A. $4$
• B. $2$
• C. $1$
• D. $8$

Answer 1

The correct option is D $8$

$x^2=8y$

On comparing the given equation with $x^2=4ay$

$a=2$

$\therefore focus=(0,a)=(0,2)$

In fig., for $y=2$,

$x^2=16\Rightarrow x=\pm 4$

Now, from the figure, OPQ represent the triangle whose area is to be determined.

$\therefore area\left(△OPQ\right)=\frac{1}{2}\times PQ\times OF=\frac{1}{2}\times 8\times 2=8\text{sq. units}$