Question

Use the information provided to write the equation of the circle. Center: (7,-2) Radius: 3

(A) (x+7)²+(y-2)² = 3
(B) (x-7)²+(y+2)² = 3
(c) (x+7)²+(y-2)² = 9
(D) (x-7)²+(y+2)² = 9

Answer 1

The equation of a circle with center at (7, -2) and radius of 3 is (x - 7)² + (y + 2)² = 9, which corresponds to option (D).

Step-by-step explanation:

To write the equation of the circle, we use the standard form of the equation of a circle, which is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is the radius. Given the center at (7, -2) and a radius of 3, we substitute these values into the standard form, yielding:

(x - 7)² + (y + 2)² = 3²

Upon simplification, we end up with:

(x - 7)² + (y + 2)² = 9

Therefore, the equation of the circle is (D) (x - 7)² + (y + 2)² = 9.