Q. $P$ is a point on either of two lines $y - \sqrt{3}|x| = 2$ at a distance 5 unit from their point of intersection. The coordinates of the foot of the perpendicular from $P$ on the bisector of the angle between them are
A) $\left( 0,\frac{4 + 5\sqrt{3}}{2} \right)\ or\ \left( 0,\frac{4 - 5\sqrt{3}}{2} \right)\ depending\ on\ which\ the\ point\ P\ is\ taken$
B) $\left( 0,\frac{4 + 5\sqrt{3}}{2} \right)$
C) $\left( 0,\frac{4 - 5\sqrt{3}}{2} \right)$
D) $\left( \frac{5}{2},\frac{5\sqrt{3}}{2} \right)$
Explanation
(b)
Given that, $y = \sqrt{3}|x| + 2$
$and\ PQ = 5,\ so,\ QR = \frac{5\sqrt{3}}{2}$
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$\therefore Coordinates\ of\ R\ are\ \left( 0,\ 2 + \frac{5\sqrt{3}}{2} \right)\ or\ \left( 0,\frac{4 + 5\sqrt{3}}{2} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.