Question

If $(-3,2)$ lies of 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. None of these
• C. 11
• D. 24

Answer 1

The correct option is A -11

Equation of circle is :

$x^2+y^2+6x+8y-5=0$

$\therefore Centre=(-3,-4)$

Circle $x^2+y^2+2gx+2fy+c=0$ has centre

(-g, -f)

Since both circles are concentric.

$\Rightarrow -g=-3and-f=-4$

$\Rightarrow g=3andf=4$

Point (-3, 2) lies on circle

$x^2+y^2+2gx+2fy+c=0$

$\Rightarrow (-3{)}^2+2^2+2g\times (-3)+2f\times 2+c=0$

$\Rightarrow 9+4-6\times 3+4\times 4+c=0$

$\Rightarrow c=-11$

Hence, option (b) is correct.