Question

If the endpoints of the diameter of a circle are (6, 3) and (2, 1), what is the standard form equation of the circle?

Answer 1

If the endpoints of a diameter are (6,3) and (2,1) the midpoint is the center of the circle so:

(x,y)=((6+2)/2, (3+1)/2)=(4,2)

Now we need to find the radius....the diameter is:

d^2=(6-2)^2+(3-1)^2

d^2=16+4

d^2=20 since d=2r, r=d/2, and r^2=d^2/4 so

r^2=5

The standard form of the circle is (x-h)^2+(y-k)^2=r^2 and we know:

(h,k)=(4,2) from earlier so:

(x-4)^2+(y-2)^2=5

Answer 2

B) (x − 4)2 + (y − 2)2 = 5

Explanation:

Substitute the endpoints (6, 3) and (2, 1) into the midpoint formula to find the center of the circle:

h = 6 + 2 2 = 4

k = 3 + 1 2 = 2

Center: (4, 2)

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 (6 − 2)2 + (3 − 1)2

r = 1 2 (2 5 )

r = 5

Substitute values into standard equation of circle:

(x − h)2 + (y − k)2 = r2

(x − 4)2 + (y − 2)2 = ( 5 )2

(x − 4)2 + (y − 2)2 = 5