# If the Equation (4a − 3) X2 + Ay2 + 6x − 2y + 2 = 0 Represents a Circle, Then Its Centre is - Mathematics

MCQ

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

#### Solution

(−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 $\left( - 3, 1 \right)$ .

Concept: Circle - Standard Equation of a Circle
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Q 4 | Page 39