Rotate These Straight Lines!

The line $\mathbb{L}$ has intercepts $a$ and $b$ on the coordinate axes. When keeping origin fix ,the coordinate axes are rotated through a fixed angle then the same line has intercepts $p$ and $q$ on the rotated axes. Then which option is correct?

$\LARGE A)$ : $\frac {1}{a^2} + \frac {1}{b^2} = \frac {1}{p^2} + \frac {1}{q^2}$

$\LARGE B)$ : $\frac {1}{a^2} + \frac {1}{p^2} = \frac {1}{b^2} + \frac {1}{q^2}$

$\LARGE C)$ : $a^2 + p^2 = b^2 + q^2$

$\LARGE D)$ : $a^2 + b^2 = p^2 + q^2$

Details and Assumptions :

• The value $\arctan \left ( \frac {3}{4} \right )$ is not used, it's just for illustration purpose.

Picture Source File: Wikimedia Rotate File