2012PP-II-26

16-06-2021 app.cch No Comments

Ans: D
Let

P = (x, x + 2)

$\begin{array}{rcl} A P & = & \sqrt{(x - 1)^{2} + (x + 2 - (- 3))^{2}} \\ = & \sqrt{2 x^{2} + 8 x + 26} \end{array}$

Also,

$\begin{array}{rcl} B P & = & \sqrt{(x - (- 5))^{2} + (x + 2 - 7)^{2}} \\ = & \sqrt{2 x^{2} + 50} \end{array}$

For $A P = P B$ , we have

$\begin{array}{rcl} 2 x^{2} + 8 x + 26 & = & 2 x^{2} + 50 \\ 8 x & = & 24 \\ x & = & 3 \end{array}$

Therefore, $P (3, 5)$ .