A tangent is drawn to each of the circles $x^{2} + y^{2} = a^{2}$ and $x^{2} + y^{2} = b^{2} ˙$ Show that if the two tangents are mutually perpendicular, the locus of their point of intersection is a circle concentric with the given circles.

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A tangent is drawn to each of the circles

x^{2} + y^{2} = a^{2}

and

x^{2} + y^{2} = b^{2} ˙

Show that if the two tangents are mutually perpendicular, the locus of their point of intersection is a circle concentric with the given circles.

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Question Text

A tangent is drawn to each of the circles

x^{2} + y^{2} = a^{2}

and

x^{2} + y^{2} = b^{2} ˙

Show that if the two tangents are mutually perpendicular, the locus of their point of intersection is a circle concentric with the given circles.

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