Question

Tangent drawn from the point $(-8,0)$ to the parabola $y^2=8x$ touch the parabola at $P$ and $Q$. If $F$ is the focus of the parabola, then the area of the triangle $PFQ$( in sq. units) is equal to

Answer 1

$P$ & $Q$ are symmetric point, so their $x-$ coordinates will be same and $y-$ coordinates will be negative of each other

Let equation of tangent $QP$ is

$y=mx+\frac{2}{m}$

It passes through $(-8,0)$ then

$\frac{-8m+2=0}{m}$

$m=1/2$

$y=\frac{1}{2}x+4$

For intersection with parabola put $y^2=8x$

$P$ cones to be $(8,8)$

then $Q(8,-8)$

$PQ=16$

Height $=FC=8-2=6$

Area of $△PFQ=\frac{1}{2}\times PQ\times PC=\frac{1}{2}\times 16\times 6=48squnits$