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Question
Find the values of a and b if the equation (a - 1)x2 + by2 + (b - 8)xy + 4x + 4y - 1 = 0 represents a circle.
Solution
Equation of the circle is (a - 1)x2 + by2 + (b - 8)xy + 4x + 4y - 1 = 0
Equation of the circle will not have (xy) term.
∴ Co-efficient of (xy) term is 0
⇒ b - 8 = 0
⇒ b = 8 ....(1)
Also, for any circle,
Co-efficient of x2 = Co-efficient of y2
⇒ a - 1 = b
⇒ a - 1 = 8
⇒ a = 9
∴ a = 9 and b = 8
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