Question

A ray parallel to the x - axis is incident at a point $P$ on a parabolic reflecting surface, and the reflected ray becomes parallel to y - axis as shown in the figure. If the equation of parabola is given by $y^2-2x=0$ , then the coordinates of point $P$ are

• A. $(1,\frac{1}{2})$
• B. $(\frac{1}{2},1)$
• C. $(\frac{3}{2},1)$
• D. $(\frac{1}{3},\frac{1}{2})$

Answer 1

The correct option is B $(\frac{1}{2},1)$


Given the equation of parabola as,$y^2=2x$

Differentiating with respect to x,
$2y\frac{dy}{dx}=2$
$\frac{dy}{dx}=\frac{1}{y}$

Now,
$\frac{1}{y}=\left(\frac{dy}{dx}\right)=\tan \theta =\tan {45}^{\circ }=1$

$\Rightarrow y=1$

Putting $y=1$ in $y^2=2x\Rightarrow x=\frac{1}{2}$