Answer 1

(−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 = \[x^2 + y^2 + 6x - 2y + 2 = 0\]

Thus, the coordinates of the centre is \[\left( - 3, 1 \right)\] .