Find the Center and Radius x^2+y^2-6y-7=0

Problem

x2+y2−6*y−7=0

Solution

1. Group the terms by variable and move the constant term to the right side of the equation.

x2+(y2−6*y)=7

2. Complete the square for the y terms by taking half of the coefficient of y which is −3 squaring it to get 9 and adding it to both sides.

x2+(y2−6*y+9)=7+9

3. Rewrite the equation in the standard form of a circle (x−h)2+(y−k)2=r2 by factoring the perfect square trinomial.

(x−0)2+(y−3)2=16

4. Identify the center (h,k) and the radius r from the standard form equation.

h=0

k=3

r2=16⇒r=4

Final Answer

Center: *(0,3), Radius: *4

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