Question

Two rays of light coming along the lines $y=1$ and $y=-2$ from the positive direction of $x-$axis and strikes a concave mirror whose intersection with the $x-y$ plane is a parabola $y^2=x$ at $A$ and $B$ respectively.The reflected rays pass through a fixed point $C,$ then the area of the $△ABC$ is

• A. $\frac{21}{8}$sq.unit
• B. $\frac{19}{2}$sq.unit
• C. $\frac{17}{2}$sq.unit
• D. $\frac{15}{2}$sq.unit

Answer 1

The correct option is A $\frac{21}{8}$sq.unit

Solving $y=1$ and $y^2=x$
then $A\equiv (1,1)$
and solving $y=-2$
and $y^2=x$
then $B\equiv (4,-2)$
$\because$ After reflection both reflected rays pass through focus of the parabola $y^2=x$
i.e.$C\equiv (\frac{1}{4},0)$
$\therefore$ Required Area$=\frac{1}{2}\left|\begin{array}{ccc}1& 1& 1\\ 4& -2& 1\\ \frac{1}{4}& 0& 1\end{array}\right|=\frac{21}{8}$ sq. unit