P (x, y), Q (-2,-3) and R (2,3) are the vertices of a right triangle PQR right angled at P. Find the relationship between x and y. Hence, find all…

In \(\displaystyle \Delta \mathrm{PQR}, \angle \mathrm{P}=90^{\circ}\) \[\begin{aligned} & P Q^{2}+P R^{2}=Q R^{2} \\ & \Rightarrow(x+2)^{2}+(y+3)^{2}+(x-2)^{2}+(y-3)^{2}=4^{2}+6^{2} \\ & \Rightarrow x^{2}+4 x+4+y^{2}+6 y+9+x^{2}-4 x+4+y^{2}-6 y+9=52 \end{aligned} \] gives, \(\displaystyle x^{2}+y^{2}=13\) Now for \(\displaystyle y=2, x= \pm 3\)