Find the center and the radius of the circle 9x2+9y22y=0


Answer:

(0,19) and 19

Step by Step Explanation:
  1. The equation of a circle with center at (a,b) and radius r is given by
    (xa)2+(yb)2=r2
  2. The given equation is
    9x2+9y22y=0x2+(y229y)=0
  3. Completing the squares within the parentheses
    x2+(y229y+181)=0+181(x0)2+(y19)2=181(x0)2+(y19)2=(19)2...(1)     
  4. 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.

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