Question

The circle below is centered at (4, -1) and has a radius of 3. What is its

equation?
O A. (x-4)2+(-1)² =9
O B. (x-4)2 + (y+ 1)² = 9
C. (x-4)2 + (y+ 1)² = 3
OD. (x-4)2 + (-1)²=3

Answer 1

The equation of the circle centered at (4, -1) with a radius of 3 is (x-4)² + (y+1)² = 9. Therefore correct option is B

Step-by-step explanation:

The equation of the circle centered at (4, -1) with a radius of 3 is represented by the option B, which is (x-4)² + (y+1)² = 9.

To understand why this is the correct answer, we can use the standard form of the equation of a circle,

(x-h)² + (y-k)² = r², where (h, k) represents the center of the circle and r represents the radius.

In this case, we have (h, k) = (4, -1) and r = 3.

Plugging these values into the standard form gives us (x-4)² + (y+1)² = 9.

This equation represents all the points that are exactly 3 units away from the center (4, -1), forming the circle.