Find the center and the radius of the circle 9x2+9y2−2y=0
Answer:
(0,19) and 19
- The equation of a circle with center at (a,b) and radius r is given by
(x−a)2+(y−b)2=r2 - The given equation is
9x2+9y2−2y=0⟹x2+(y2−29y)=0 - Completing the squares within the parentheses
⟹x2+(y2−29y+181)=0+181⟹(x−0)2+(y−19)2=181⟹(x−0)2+(y−19)2=(19)2...(1) - On comparing eq(1) with the standard form of the equation of the circle, we get,
⟹a=0,b=19, and r=19
Hence, the center of the circle is (0,19) and the radius of the circle is 19.