A point moves such that the sum of the square of the distances from two fixed straight lines int...

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A point moves such that the sum of the square of the distances from two fixed straight lines intersecting at angle \( 2 \alpha \) is a constant. Prove that the locus is an ellipse of eccentricity
\[
\frac{\sqrt{\cos 2 \alpha}}{\cos \alpha} \text { if } \alpha\frac{\pi}{4} \text { and } \frac{\sqrt{-\cos 2 \alpha}}{\sin \alpha} \text { if } \alpha\frac{\pi}{4}
\]
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