I need help asap
Which equation represents a circle with diameter endpoints at (−3,−2) and (1,−4)?

A

(x−1)2+(y−3)2=20

B

(x+1)2+(y+3)2=5

C

(x+1)2+(y+3)2=20

D

(x−1)2+(y−3)2=5

Option C: is the equation of the circle.

Explanation:

Given that the endpoints of the circle are at (-3,-2) and (1,-4)

The equation of the circle can be determined using the formula,

where are the coordinates of the center and r is the radius.

Center:

The center of the circle can be determined using the midpoint formula,

Substituting the coordinates (-3,-2) and (1,-4) in the above formula, we get,

Thus, the center of the circle is at (-1,-3)

Radius:

The radius of the circle can be determined using the distance formula,

Substituting the coordinates (-3,-2) and (1,-4) in the above formula, we get,

Thus, the radius of the circle is

Equation of the circle:

Substituting the center and the radius of the circle in the equation , we get,

Simplifying, we get,

Therefore, the equation of the circle is

Hence, Option C is the correct answer.