Answer:
Step-by-step explanation:
The standard form equation of a circle with radius r is expressed as
( x − h )^2 + ( y − k )^2 =r ^2 ,
where r represents the radius
h and k are the coordinates of the center of the circle C( h , k )
To determine the coordinates at the center of the circle, the midpoint formula would be used. It is expressed as
[(x1 + x2)/2 , (y1 + y2)/2]
Midpoint of the circle =
(6 - 4)/2 , (2 + 7)/2 = (1, 4.5)
h coordinate of the center = 1
k coordinate of the center = 4.5
r^2 = (x - h)^2 + (2 - k)^2
r^2 = (6 - 1)^2 + (2 - 4.5)^2
r^2 = 5^2 + (- 2.5)^2 = 25 + 6.25
r^2 = 31.25
Substituting r^2 = 31.25, h = 1 and k = 4.5 into (x − h )^2 + ( y − k )^2 = r^2, the standard equation of the circle becomes
(x − 1 )^2 + ( y − 4.5 )^2 = 31.25
