1. The equation x² + y² = 81 is in standard form for a circle centered at the origin (0,0). The radius of the circle is the square root of 81, which is 9.
Therefore, the center is at (0,0) and the radius is 9.
2. To put this equation in standard form for a circle, we must complete the square for both x and y terms.
x² + 6x + y² - 8y = 75
(x² + 6x + 9) + (y² - 8y + 16) = 100
(x + 3)² + (y - 4)² = 100
This equation is now in standard form for a circle. The center of the circle is (-3,4) and the radius is the square root of 100, which is 10.
Therefore, the center is (-3,4) and the radius is 10.
Answers & Comments
1. The equation x² + y² = 81 is in standard form for a circle centered at the origin (0,0). The radius of the circle is the square root of 81, which is 9.
Therefore, the center is at (0,0) and the radius is 9.
2. To put this equation in standard form for a circle, we must complete the square for both x and y terms.
x² + 6x + y² - 8y = 75
(x² + 6x + 9) + (y² - 8y + 16) = 100
(x + 3)² + (y - 4)² = 100
This equation is now in standard form for a circle. The center of the circle is (-3,4) and the radius is the square root of 100, which is 10.
Therefore, the center is (-3,4) and the radius is 10.