Find the center and the radius of the circle 5x2+5y22x=0


Answer:

(15,0) and 15

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
    5x2+5y22x=0x2+y225x=0(x225x)+y2=0
  3. Completing the squares within the parentheses
    (x225x+125)+y2=0+125(x15)2+(y0)2=125(x15)2+(y0)2=(15)2     ...(1)
  4. On comparing eq(1) with the standard form of the equation of the circle, we get,
    a=15,b=0, and r=15
    Hence, the center of the circle is (15,0) and the radius of the circle is 15.

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