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Question

If the equation ax2 + (2 – b) xy + 3y2 – 6bx + 30y + 6b = 0 represents a circle, then a = __________, b = __________.

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Solution

Since ax2 + (2 – b) xy + 3y2 – 6bx + 30y + 6b = 0 represent circle
2 – b = 0 (∵ xy term has coefficient equal to zero always)
i.e. b = 2
and a = 3 (∵ coefficient of x2 = coeffcient of y2 in case of circle)

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