Answer:
Center: (4,-2)
Radius: 2√3 units
Explanation:
We wish to find the center and radius of the equation x²+y²-8x+2y=-8
Step 1: Complete the square for both variables:
x²+y²-8x+2y=-8
x²-8x+y²+2y=-8 (Rearrange)
x²-8x+16+y²+2y+4=-8+16+4 (Add to both sides)
(x-4)²+(y+2)²=12 (Reduce trinomials)
Step 2: Interpret the center and radius of the circle:
The equation of a circle is (x-h)²+(y-k)²=r² where (h,k) is the center of the circle and r is the radius of the circle. Since (h,k) translates to (4,-2), this means the center of the circle is (4,-2). Since r²=12, then r=√12=2√3 units