The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5). what is the center point

Question

 fill in the blank           The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).

The center of the circle is at the point ___
, and its radius is ____ units. The equation of this circle in standard form is____

Answer 1

the longest chord is the diameter

the center of the circle is x=(4+4)/2=4 and y=(10.5+5.5)/2=8

the center is (4,8)

one diameter is on the line x=4 and y goes from 5.5 to 10.5 for a distance of 5 units

therefore the diameter is 5 units and the radius is 2.5 units

also, you could get the answer by using the distance formula using the center and one of the endpoints of the diameter

use (4,8) and (4,10.5)

√((4-4)^2+(10.5-8)^2)

√2.5^2

2.5 units again

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

(x-4)^2+(y-8)^2=2.5^2

(x-4)^2+(y-8)^2=6.25 is the equation of the circle