Find the Center and Radius x^2+y^2-4x-14y+50=0

Problem

x2+y2−4*x−14*y+50=0

Solution

1. Group the x terms and y terms together and move the constant term to the right side of the equation.

x2−4*x+y2−14*y=−50

2. Complete the square for the x terms by adding ((−4)/2)2=4 to both sides.

(x2−4*x+4)+y2−14*y=−50+4

3. Complete the square for the y terms by adding ((−14)/2)2=49 to both sides.

(x2−4*x+4)+(y2−14*y+49)=−50+4+49

4. Simplify the right side and write the left side as squared binomials.

(x−2)2+(y−7)2=3

5. Identify the center (h,k) and the radius r from the standard form (x−h)2+(y−k)2=r2

h=2

k=7

r2=3⇒r=√(,3)

Final Answer

Center: *(2,7), Radius: √(,3)

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