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If the endpoints of the diameter of a circle are (6, 3) and (2, 1), what is the standard form equation of the circle?
A) (x + 4)2 + (y + 2)2 = 5
B) (x − 4)2 + (y − 2)2 = 5
C) (x + 4)2 + (y + 2)2 = ✔️ 5
D) (x − 4)2 + (y − 2)2 = ✔️ 5

Respuesta :

the center of the circle = (6 + 2)/2 ,  (3 + 1)/2  = (4,2)

diameter = sqrt ( (6-2)^2 + (3-1)^2 ) = sqrt20

radius 1/2 * sqrt20 =  1/2 * 2 * sqrt5 = sqrt 5
r^2 = 5  

so the required equation is:-
(x - 4)^2 + (x - 2)^2 = 5


Its D

Answer:

D

Step-by-step explanation:

(x − 6)2 + (y + 4)2 = 8

Substitute the endpoints (8, −6) and (4, −2) into the midpoint formula to find the center of the circle:

h =  

8 + 4

2

= 6

k =  

−6 + (−2)

2

= −4

Center: (6, −4)

Use the distance formula to find the length of the radius. Remember that the radius is  

1

2

the length of the diameter:

r =  

1

2

(8 − 4)2 +(−6 − (−2))2

r =  

1

2

(4

2

)

r = 2

2

Substitute values into standard equation of circle:

(x − h)2 + (y − k)2 = r2

(x − 6)2 + (y − (−4)2 = (2

2

)2

(x − 6)2 + (y + 4)2 = 8

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