Find The Equations Of The Circle Which Passes Through The Origin And Cut Off Chords Of Length A From Each Of The Lines y = x and y = –x.

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Question

Find the equations of the circle which passes through the origin and cut off chords of length a from each of the lines y = x and y = –x.

medium

Solution

Correct option is

Let the required circle be

x² + y² + 2gx + 2fy + c = 0

which passes through (0, 0) then c = 0

∴ x² + y² + 2gx + 2fy = 0 …(1)

Point of intersection of the circle (1) and the line y = x are obtained by solving

x² + x² + 2gx + 2fx = 0

These point are A(0, 0) and B(–g, –f, –g – f )

Similarly points of intersection of the circle (1) and the line

y = –x are C(0, 0) and D(f – g, g – f)

∴ Required equations are

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