Question

geometryyyyyyyy!!!!!!!!!!!!!!!
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

Answer 1

Answer:

B $(x+1)^{2}$ + $(y+3)^{2}$ = 5

Step-by-step explanation:

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

We know that the equation of circle is

$(x-h)^{2}$ + $(y-k)^{2}$ = $r^{2}$

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

(  $\frac{x1+x2}{2}$ , $\frac{y1+y2}{2}$ )

( $\frac{-3+1}{2}$ , $\frac{-2-4}{2}$ )

(-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

$(1+1)^{2}$ + $(-4+3)^{2}$ = $r^{2}$

$r^{2}$ = 5

Substituting the values of (h,k) and $r^{2}$, we get the equation of circle as

$(x+1)^{2}$ + $(y+3)^{2}$ = 5

Hence the answer is B