To identify the center and radius of the circle given by the equation (x-16)² + (y+14) = 1, we need to rewrite the equation in the standard form for a circle, which is (x - h)² + (y - k)² = r², where (h,k) represents the center of the circle and r represents the radius.
1. Given equation: (x - 16)² + (y + 14) = 1
2. To rewrite it in standard form, we need to expand the squared terms:
(x - 16)² = x² - 32x + 256
(y + 14)² = y² + 28y + 196
3. Substitute the expanded terms back into the equation:
x² - 32x + 256 + y² + 28y + 196 = 1
4. Combine like terms:
x² + y² - 32x + 28y + 452 = 1
5. Rearrange the terms to match the standard form:
x² - 32x + y² + 28y = -451
6. Now, complete the square for x and y terms:
(x - 16)² - 256 + (y + 14)² - 196 = -451
7. Simplify:
(x - 16)² + (y + 14)² = 9
8. Compare with the standard form:
Center = (16, -14) (opposite signs of the numbers inside the parentheses)
Radius = √9 = 3
Therefore, the center of the circle is at (16, -14) and the radius is 3 units.
