Question

$P(\sqrt{2},\sqrt{2})$ is a point on the circle $x^2+y^2=4$ and $Q$ is another point on the circle such that $arcPQ=\frac{1}{4}\times$ circumference. The coordinates of $Q$ are

• A. $(-\sqrt{2},-\sqrt{2})$
• B. $(\sqrt{2},-\sqrt{2})$
• C. $(-\sqrt{2},\sqrt{2})$
• D. none of these

Answer 1

Answer: (B), (C)

$(-\sqrt{2},\sqrt{2})$
$(\sqrt{2},-\sqrt{2})$

Given circle ,$x^2+y^2=4$
$Radius=2$
$ArcPQ=\frac{1}{4}\times \left(2\pi r\right)$
Hence, $PQ$ subtends a right angle at the centre.
The parametric angle of point P is $\frac{\pi }{4}$ .Hence the parametric angle of point Q will be $\frac{3\pi }{4}$ or $\frac{-\pi }{4}$
Thus, the coordinates of Q can be $(-\sqrt{2},\sqrt{2})$ or $(\sqrt{2},-\sqrt{2})$
Hence, options 'B' and 'C' are correct.