Question

Tangents are 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. $64$
• B. $24$
• C. $32$
• D. $48$

Answer 1

The correct option is D $48$

Let $TP$ and $TQ$ are the tangents to the given parabola $y^2=8x$
Equation of tangent for parabola is
$T=0\Rightarrow y{y}_1=4(x+x_1)$
It passes through $(-8,0)$
$\Rightarrow y_1\cdot 0=4(-8+x_1)\Rightarrow x_1=8\Rightarrow y_1=\pm 8$
So, the coordinates of $P$ and $Q$ are $(8,8)$ and $(8,-8)$


Focus of parabola is $F(2,0)$ and $M$ is the mid-point of $PQ$
So, the coordinates of $M=(8,0)$
$\therefore$ Area of $△PFQ$
$=\frac{1}{2}\times (8-2)\times 16=48\text{sq. units}$