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  4. The condition that the chord x cos α+y sin α-p=0 of x2+y2-a2=0 may subtend a right angle at the center of the circle is

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Q. The condition that the chord $x \cos \alpha+y \sin \alpha-p=0$ of $x^{2}+y^{2}-a^{2}=0$ may subtend a right angle at the center of the circle is

Conic Sections

Solution:

The distance of the given line from the center of the circle is $|p|$.
Now, the line subtends right angle at the center. Hence,
Radius $=\sqrt{2}|p|$
or $a=\sqrt{2}|p|$
or $a^{2}=2 p^{2}$