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 s units) is equal to :

• A. 24
• B. 32
• C. 48
• D. 64

Answer 1

Answer: (C)

48

Answer 2

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 $\Delta PFQ = \frac{1}{2}\times16\times6 = 48$ sunits.