A diameter of a circle has endpoints (–3, 7) and (5, 7). Determine the equation of the circle. Center: (1, 7) Radius: 4

Question

answer choices:

(x – 1)² + (y – 7)² = 16

(x – 1)² + (y – 7)² = 8

(x – 2)² + (y – 14)² = 4

(x + 3)² + (y – 5)² = 8

this is for geometry lesson probability, it would greatly appreciated if someone could help me.

Answer 1

The equation of a circle with center (a,b) and radius r is

(x - a)² + (y - b)² = r²

Here, a = 1,, b = 7, and r = 4. Since 4² = 16, the equation is

(x - 1)² + (y - 7)² = 16.

Answer 2

The center of (1,7) gives you the left side of the equation

(x – 1)² + (y – 7)² =

The radius of 4 gives the right side of the equation. r² = 16

The correct answer is A.

Answer 3

This problem statement gives plenty to work with.

Note that the formula for the equation of a circle with a center at point (h,k) and radius r is:

(x-h)² + (y-k)² = r²

For this problem, this is:

(x-1)² + (y-7)² = 4²

Note that 4² is 16.

Now, you may also check to see whether the endpoints of the diameter fit any of the equations.

Is (-3-1)² + (7-7)² = 4² ?

16 = 16 ? yes

Is (5-1)² + (7-7)² = 4² ?

16 = 16 ?yes

Is (-3– 1)² + (7 – 7)² = 8 ?

. . . (others are no)