A Line Meets The Co-ordinate Axes At A and B. A Circle Is Circumscribed About The Triangle OAB. If The Distance Of The Points A and B from The Tangent At O, The Origin, To The Circle Are m and n respectively, Find The Equation Of The Circle.

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Question

A line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB. If the distance of the points A and B from the tangent at O, the origin, to the circle are m and n respectively, find the equation of the circle.

diffcult

Solution

Correct option is

Let OA = a and OB = b then the co-ordinates of A and B are

(a, 0) and (0, b) respectively.

Since ∠AOB = π/2

Hence AB is the diameter of the required circle whose equation is

Equation of tangent at (0, 0) of (1) is

or ax + by = 0

Adding (2) and (3), we get

From (2) and (3), we get

From (1), equation of required circle is

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