Find the center and the radius of the circle 5x2+5y2−2x=0
Answer:
(15,0) and 15
- 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
5x2+5y2−2x=0⟹x2+y2−25x=0⟹(x2−25x)+y2=0 - Completing the squares within the parentheses
⟹(x2−25x+125)+y2=0+125⟹(x−15)2+(y−0)2=125⟹(x−15)2+(y−0)2=(15)2 ...(1) - 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.