From a fixed point on x 2 + y 2 = a 2 , two tangents are drawn to x 2 + y 2 = b 2 ( a b ) . If their chord of contact touches a variable circle through the origin, what is the locus of the variable

Question

From a fixed point on x 2 + y 2 = a 2 , two tangents are drawn to x 2 + y 2 = b 2 ( a > b ) . If their chord of contact touches a variable circle through the origin, what is the locus of the variable circle centre?

TestHub · Accepted Answer

The chord of contact is a fixed line. A circle through the origin has radius equal to its centre distance from the origin; tangency to the fixed line makes its centre equidistant from this line and the origin, which is a parabola.

Mathematics - Circle Question with Solution | TestHub

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