Question

Which of the following equations represents a circle with centre $(g,f)$ and radius $\sqrt{g^2+f^2+c}$ ?

• A. $x^2+y^2+2gx+2fy+c=0$
• B. $x^2+y^2-2gx-2fy+c=0$
• C. $x^2+y^2+2gx+2fy-c=0$
• D. $x^2+y^2-2gx-2fy-c=0$

Answer 1

The correct option is D

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

Equation of a circle with centre $(h,k)$ and radius r is given by
$(x-h{)}^2+(y-k{)}^2=r^2$

Given, the centre is $(g,f)$ and radius is $\sqrt{g^2+f^2+c}$

$\Rightarrow (x-g{)}^2+(y-f{)}^2=(\sqrt{g^2+f^2+c}{)}^2$

$\Rightarrow x^2+y^2-2gx-2fy+g^2+f^2=g^2+f^2+c$

$\Rightarrow x^2+y^2-2gx-2fy-c=0$