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Question

If the equation (4a − 3) x2 + ay2 + 6x − 2y + 2 = 0 represents a circle, then its centre is
(a) (3, −1)
(b) (3, 1)
(c) (−3, 1)
(d) none of these

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Solution

(c) (−3, 1)

If the equation (4a − 3) x2 + ay2 + 6x − 2y + 2 = 0 represents a circle, then we have:
Coefficient of x2 = Coefficient of y2
4a-3=a
⇒ a = 1

∴ Equation of the circle = x2+y2+6x-2y+2=0

Thus, the coordinates of the centre is -3, 1.

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