Question

Let a parabola $P$ be such that its vertex and focus lie on the positive $x$-axis at a distance $2$ and $4$ units from the origin, respectively. If tangents are drawn from $O(0,0)$ to the parabola $P$ which meet $P$ at $S$ and $R$, then the area (in sq. units) of $\Delta SOR$ is equal to

• A. $16$
• B. $32$
• C. $16\sqrt{2}$
• D. $8\sqrt{2}$

Answer 1

The correct option is A $16$

From given condition $y-$axis is directrix and equation of parabola is
$y^2=8(x-2)$



Let $y=mx$ be tangent
$\therefore m^2{x}^2-8x+16=0\Rightarrow m=\pm 1$
So that lines $y=x$ and $y=-x$ are tangents.
$\therefore$ Coordinate of $S$ and $R$ be $(4,4)$ and $(4,-4)$
$\therefore$ Area of $△SOR=(\frac{1}{2}\times 4\times 4)\times 2=16$