Rotate These Straight Lines!

Geometry Level 3

543543

543543

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

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