Question

Find the centre and radius of $x^2+y^2+6y=0$.

• (A) $(0,3),3$
• (B) $(-3,0),3$
• (C) $(3,0),3$
• (D) $(0,-3),3$

Answer 1

The Correct Option is D

Explanation:
Given,$x^2+y^2+6y=0$$\Rightarrow x^2+y^2+6y+9-9=x^2+(y+3{)}^2-9=0$$\Rightarrow x^2+(y+3{)}^2=9$Standard equation of the circle with radius $r$ and centre $(h,k)$ is given by$(x-h{)}^2+(y-k{)}^2=r^2$By comparing, we get$h=0,k=-3,r=3$$\therefore$ Centre$=(0,-3),$ Radius $=3$Hence, the correct option is (D).