Question

If the equation $(4a-3)x^2+a{y}^2+6x-2y+2=0$ represents a circle, then its centre is

• A. (3, -1)
• B. (3, 1)
• C. (-3, -1)
• D. None of these

Answer 1

The correct option is C

(-3, -1)

If the equation $(4a-3)x^2+a{y}^2+6x-2y+2=0$ represents a circle, then we have:

Coefficient of $x^2=$ Coefficient of $y^2$

$\Rightarrow 4a-3=a$

$\Rightarrow a=1$

$\therefore$ Equation of the circle

$=x^2+y^2+6x-2y+2=0$

Thus, the coordinate of the centre is (-3,1)