Final answer:
The equation for a circle with center at (0,6) and radius 9 is x² + (y - 6)² = 81.
Step-by-step explanation:
To find an equation for a circle with the center at (0,6) and a radius of 9, we use the standard form equation for a circle:
(x - h)² + (y - k)² = r²,
where (h,k) is the center of the circle and r is its radius. Plugging in our specific values, we obtain:
(x - 0)² + (y - 6)² = 9²
After simplifying, the equation becomes:
x² + (y - 6)² = 81.
This is the equation of the circle centered at (0,6) with a radius of 9.
The equation for a circle with center (h, k) and radius r is given by the formula: (x - h)² + (y - k)² = r². In this case, the center of the circle is (0,6) and the radius is 9. Substituting these values into the equation, we get: (x - 0)² + (y - 6)² = 9².
Expanding the equation, we have: x² + y² - 12y + 36 = 81. Rearranging the terms, the equation of the circle is: x² + y² - 12y - 45 = 0.