Q. 45.0( 1 Vote )

# If the equation (4a – 3) x2 + ay2 + 6x – 2y + 2 = 0 represents a circle, then its centre isA. (3, - 1)B. (3,1)C. (- 3,1)D. none of these

Given that the equation of the circle is:

(4a - 3)x2 + ay2 + 6x - 2y + 2 = 0 ..... (1)

Comparing with the standard equation of circle:

x2 + y2 + 2ax + 2by + c = 0

We get

4a - 3 = a

4a - a = 3

a = 1

Substituting a value in (1), we get

(4(1) - 3)x2 + 1y2 + 6x - 2y + 2 = 0

x2 + y2 + 6x - 2y + 2 = 0

We know that for a circle x2 + y2 + 2ax + 2by + c = 0

Centre = (- a, - b)

Radius = Centre(C) =  The correct option is (c)

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