Question

what is the equation of a circle whose radius is 4 cm and which is concentric with the circle x2+y2+2x-6y=0​

Answer 1

The equation of a circle whose radius is 4 cm and which is concentric wih the circle $x^{2}+y^{2}+2x-6y=0$ is $x^{2}+y^{2}+2x-6y-6=0$

• Given circle is

                 $x^{2}+y^{2}+2x-6y=0------------(1)$

• Equation of circle concentric with (1) is given by

                 $x^{2}+y^{2}+2x-6y+k=0-----------(2)$

• Given,

                  Radius = 4 cm

                  $\sqrt{g^{2}+f^{2}-k}=4$

                  2g = 2 ⇒ g = 1

                  2f = - 6 ⇒ f = - 3

                   $\sqrt{1^{2}+(-3)^{2}-k}=4$

                    $\sqrt{10-k}=4$

• Squaring on both sides

                     $10-k=16$

                     $-k=6$

                       $k=-6$

• Substituting k in (2), we get

                  $x^{2}+y^{2}+2x-6y-6=0$