Question

The equation of the circle concentric with the circle $x^2+y^2-8x+6y-5=0$ and passing through the point $(-2,-7)$ is

• A. $x^2+y^2-8x+6y-30=0$
• B. $x^2+y^2-8x+6y-26=0$
• C. $x^2+y^2-8x+6y-27=0$
• D. $x^2+y^2-8x+6y=0$

Answer 1

The correct option is C $x^2+y^2-8x+6y-27=0$

Given circle :
$x^2+y^2-8x+6y-5=0$
Any concentric circle is written as
$x^2+y^2-8x+6y+k=0$
Above circle passes through $(-2,-7)$
$\therefore 4+49+16-42+k=0$
$\Rightarrow k=-27$
$\therefore$ Equation of circle is
$x^2+y^2-8x+6y-27=0$