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Question
Find the equation of the circle which passes through the origin and cuts off intercepts aand b respectively from x and y - axes.
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Solution
Case I:
If the required circle passes through the origin and (a, b), then the end points of the diameter of the circle will be (0, 0) and (a, b).
∴ Required equation of circle: \[\left( x - 0 \right)\left( x - a \right) + \left( y - 0 \right)\left( y - b \right)\] or
If the required circle passes through the origin and (−a, −b), then the end points of the diameter of the circle will be (0, 0) and (−a, −b).
∴ Required equation of circle: \[\left( x - 0 \right)\left( x + a \right) + \left( y - 0 \right)\left( y + b \right)\] or
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