Q. 225.0( 2 Votes )

# If (- 3, 2) lies on the circle x^{2} + y^{2} + 2gx + 2fy + c = 0 which is concentric with the circle x^{2} + y^{2} + 6x + 8y – 5 = 0, then c =

A. 11

B. - 11

C. 24

D. none of these

Answer :

Given that the point (- 3,2) lies on the circle x^{2} + y^{2} + 2gx + 2fy + c = 0 which is concentric with x^{2} + y^{2} + 6x + 8y - 5 = 0.

We know that concentric circles will have same centre.

Let us assume the concentric circle be x^{2} + y^{2} + 6x + 8y + d = 0. ..... - (ii)

Substituting (- 3,2) in (ii)

⇒ (- 3)^{2} + 2^{2} + 6(- 3) + 8(2) + d = 0

⇒ 9 + 4 - 18 + 16 + d = 0

⇒ d = - 11

Substituting value of c in (ii) we get

⇒ x^{2} + y^{2} + 6x + 8y - 11 = 0

Comparing with x^{2} + y^{2} + 2gx + 2fy + c = 0 we get c = - 11

∴ The correct option is (b).

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