Final answer:
The equation of the circle with center (-2, 35) and radius 12 is given by (x + 2)² + (y - 35)² = 144.
Step-by-step explanation:
To find the equation of the circle with center (-2, 35) and radius 12, we use the standard form of the equation for a circle which is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is its radius.
Substituting our given values, the equation of the circle becomes:
(x + 2)² + (y - 35)² = 12²
Simplifying, the equation of the circle is:
(x + 2)² + (y - 35)² = 144
This is the standard form equation of the circle with the given center (-2, 35) and radius 12.