Question

Let the tangent to the parabola $S:y^2=2x$ at the point $P(2,2)$ meet the $x-$axis at $Q$ and normal at it meet the parabola $S$ at the point $R.$ Then the area (in sq. units) of the triangle $PQR$ is equal to

• A. $\frac{25}{2}$
• B. $\frac{15}{2}$
• C. $\frac{35}{2}$
• D. $25$

Answer 1

The correct option is A $\frac{25}{2}$



Tangent to $y^2=2x$ at $P(2,2)$ is $T=0$
$\Rightarrow 2y=x+2$
$\therefore Q(-2,0)$
Normal at $P(2,2)$ is $y+2x=6$ meets the curve at $R(\frac{9}{2},-3)$
Area of $△PQR=\left|\begin{array}{c}\frac{1}{2}\left|\begin{array}{ccc}2& 2& 1\\ -2& 0& 1\\ \frac{9}{2}& -3& 1\end{array}\right|\end{array}\right|$
$=\frac{25}{2}$ sq.units