If the equation (4a - 3) x^2+ ay^2+ 6x - 2y + 2 = 0 represents a … - Vidyadip

MCQ

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

A
$(3, -1)$
B
$(3, 1)$
✓
$(-3, 1)$
D
None of these

✓

Answer

Correct option: C.

$(-3, 1)$

If the equation $(4a - 3) x^2+ ay^2+ 6x - 2y + 2 = 0$ 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 coordinates of the centre is $(-3, 1).$

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