Center= (-1,1)
Radius= 3
Explanation:
x^2+y^2+2x-2y-7=0
=x2+y2+2x−2y−7=0
=x2+y2+2x-2y-7=0
Add
7
7 to both sides of the equation.
x2+y2+2x−2y=7
x2+y2+2x-2y=7
Complete the square for
x2+2x
(x+1)2−1) (x+1)2-1)
(x+1²)-1
Substitute
(x+1)2−1(x+1)2-1 for
x2+2x
x2+2x in the equation
x2+y2+2x−2y=7
x2+y2+2x-2y=7.
(x+1)²−1+y²−2y=7
=(x+1)2-1+y2-2y=7
Move -1 to the right side of the equation by adding 1 to both sides.
(x+1)2+y2−2y=7+1
(x+1)2+y2-2y=7+1
Complete the square for
y²−2y
y²-2y.
=(y−1)²−1
(y-1)²-1
Substitute (y-1)2-1 for y2-2y in the equation
x2+y2+2x−2y=7
x²+y²+2x-2y=7.
=(x+1)²+(y−1)²−1=7
Move -1 to the right side of the equation by adding 1 to both sides.
(x+1)²+(y-1)²=7+1+1
Simplify
7+1+1.
=(x+1)2+(y-1)2=9
This is the form of a circle. Use this form to determine the center and radius of the circle.
(x-h)²+(y-k)²=r2
Match the values in this circle to those of the standard form. The variable r
r represents the radius of the circle,
h represents the x-offset from the origin, and
k represents the y-offset from origin.
r=3
h=-1
k=1
The center of the circle is found at
(h,k).
Center:
(-1,1)
These values represent the important values for graphing and analyzing a circle.
Center: (-1,1)