Tangents drawn from the point (-8,0) to the parabola y^2=8x touch the parabola at P and Q.

Question

Tangents 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

Accepted Answer

$a=2$; chord of contact from $(-8,0)$: $y(0)=4(x-8)\Rightarrow x=8$. Then $y^2=64\Rightarrow y=\pm8$: $P=(8,8),Q=(8,-8)$.

Focus $F=(2,0)$; base $PQ=16$, height $=|8-2|=6$:

$$\text{Area}=\frac12(16)(6)=48.$$

Solutions · 1