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

B + = 5

Step-by-step explanation:

Given the diameter endpoints of circle: (-3,-2) and (1, -4)

We know that the equation of circle is

+ =

where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.

To find (h,k): the center is midpoint of diameter

Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by

(   , )

( , )

(-1,-3)

Hence (h,k) is (-1,-3)

Substituting values of (h.k) and (x.y) as (-1,-3) and (1,-4) respectively in equation of circle, we get

+ =

= 5

Substituting the values of (h,k) and , we get the equation of circle as

+ = 5

Hence the answer is B

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!