Answer:
(x - 3)² + (y + 1)² = 65
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
The centre C is at the midpoint of the endpoints of the diameter.
Using the midpoint formula to find C
C = ( [tex]\frac{7-1}{2}[/tex], [tex]\frac{6-8}{2}[/tex] ) = ( [tex]\frac{6}{2}[/tex], [tex]\frac{-2}{2}[/tex] ) = (3, - 1 )
The radius is the distance from the centre to either of the endpoints of the diameter.
Using the distance formula to find r
with C (3, - 1 ) and (7, 6 ) , then
r = [tex]\sqrt{(7-3)^2+(6+1)^2}[/tex]
= [tex]\sqrt{4^2+7^2}[/tex]
= [tex]\sqrt{16+49}[/tex]
= [tex]\sqrt{65}[/tex]
Then equation of circle is
(x - 3)² + (y - (- 1) )² = ([tex]\sqrt{65}[/tex] )², that is
(x - 3)² + (y + 1)² = 65 ← equation of circle
