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. $48$
• B. $32$
• C. $24$
• D. $64$

Answer 1

The correct option is A $48$

Equation of the chord of contact PQ is given by $T=0$

$T\equiv 4(x+x_1)-y{y}_1=0$, where $(x_1,y_1)\equiv (-8,0)$

$\therefore$ chord of contact is $x=8$

Coordinates of point P and Q are $(8,8)$ and $(8,-8)$

Focus of the parabola is $F(2,0)$

Area of triangle $PQF=\frac{1}{2}\times (8-2)\times (8+8)=48$ sq. units