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Question
Find the equation of the circle whose diameter is the line segment joining (−4, 3) and (12, −1). Find also the intercept made by it on y-axis.
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Solution
It is given that the end points of the diameter of the circle are (−4, 3) and (12, −1).
∴ Required equation of circle: \[\left( x + 4 \right)\left( x - 12 \right) + \left( y - 3 \right)\left( y + 1 \right)\]
or
y2 − 2y − 51 = 0
⇒ y2 − 2y − 51 = 0
⇒ \[y = 1 \pm 2\sqrt{13}\]
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