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Question
If the equation (4a − 3) x2 + ay2 + 6x − 2y + 2 = 0 represents a circle, then its centre is ______.
Options
(3, −1)
(3, 1)
(−3, 1)
none of these
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Solution
If the equation (4a − 3) x2 + ay2 + 6x − 2y + 2 = 0 represents a circle, then its centre is (−3, 1).
Explanation:
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
= \[x^2 + y^2 + 6x - 2y + 2 = 0\]
Thus, the coordinates of the centre is \[\left( - 3, 1 \right)\].
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