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 :

• A. 24
• B. 32
• C. 48
• D. 64

Answer 1

Answer: (C)

Equation of tangent for parabola $y^2=8x$
$y=mx+\frac{2}{m}$
tangent passing through $\left(-8,0\right)$
$0=-8m+\frac{2}{m}$
$m^2=\frac{1}{4}$
$m=\pm \frac{1}{2}$
for point $P\left(\frac{a}{m^2},\frac{2a}{m}\right)=\left(\frac{2}{1/2},\frac{4}{1/2}\right)=\left(8,8\right)$
$Q\left(\frac{2}{1/4},\frac{4}{-1/2}\right)=\left(8,-8\right)$
Area of $\Delta PFQ=\frac{1}{2}\times 16\times 6=48$ sq.units.