$P$ is a point on the segment joining the feet of two vertical poles of heights $a$ and $b$. The angles of elevation of the tops of the poles from P are $45^{\circ}$ each. Then the square of the distance between the tops of the poles is :

Question

$$\begin {array} {1 1} (1)\;\frac{a^2+b^2}{2} & \quad (2)\;a^2+b^2 \\ (3)\;2(a^2+b^2) & \quad (4)\;4(a^2+b^2) \end {array}$$