Final answer:
The equation x²+y²-16x+12y=0, after completing the square, represents a circle with a center at (8, -6) and a radius of 10.
Step-by-step explanation:
To graph the equation x²+y²-16x+12y=0, we must first complete the square for both x and y terms. Completing the square involves taking the coefficient of the x term (or y term), dividing it by 2, squaring it, and adding it inside the bracket after x (or y) term.
Group x and y terms: (x²-16x) + (y²+12y) = 0.
Now complete the square for each group:
For the x terms: (x-8)² since (-8)² = 64.
For the y terms: (y+6)² since (+6)² = 36.
Add these squares to both sides:
(x-8)² + (y+6)² = 64 + 36
Simplify the equation:
(x-8)² + (y+6)² = 100
This equation is now in the standard form of a circle: (x-h)² + (y-k)² = r², w