The $x$-coordinate of a point $P$ is twice its $y$-coordinate. If $P$ is equidistant from $Q(2,-5)$

Question

The $x$-coordinate of a point $P$ is twice its $y$-coordinate. If $P$ is equidistant from $Q(2,-5)$ and $R(-3,6)$, then the coordinates of $P$ are\

Professor PC Thomas Classes · Answer

(d) : Let $y$-coordinate of point $P=t$ So, $x$-coordinate of point $P=2 t$\ $\therefore \quad$ Point is $P(2 t, t)$.\ Given, $P Q=R P \Rightarrow P Q^{2}=R P^{2}$\ $\Rightarrow \quad(2 t-2)^{2}+(t+5)^{2}=(2 t+3)^{2}+(t-6)^{2}$\[0pt] [By distance formula]\ $\Rightarrow 4 t^{2}-8 t+4+t^{2}+10 t+25=4 t^{2}+12 t+9+t^{2}-12 t+36$\ $\Rightarrow 2 t=16 \Rightarrow t=8$\ $\therefore \quad$ Coordinates of $P$ are $(16,8)$.\