Q. The image of the centre of the circle $x^{2} + y^{2} = a^{2}$ with respect to the mirror $x + y = 1$ is
A) $\left( \frac{1}{\sqrt{2}},\ \sqrt{2} \right)$
B) $(\sqrt{2},\ \sqrt{2})$
C) $(\sqrt{2},\ 2\sqrt{2})$
D) None of these
Explanation
(d)
Let $P$ be image of the origin in the line $x + y = 1$
Since, $OA = OB$, therefore $\mathcal{Q}$ is the mid point of $AB$
$\therefore$ Coordinates of $\mathcal{Q}$ are $\left( \frac{1}{2},\frac{1}{2} \right)$
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Let the coordinates of $P$ be $(x_{1},\ y_{1})$
Since, $\mathcal{Q}$ is the mid point of $OP$
$\therefore\ \ \ \frac{0 + x_{1}}{2} = \frac{1}{2}and\frac{0 + y_{1}}{2} = \frac{1}{2}\ \Rightarrow \ x_{1} = 1,\ y_{1} = 1$
$\therefore$ The coordinates of $P$ are (1, 1)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.