Respuesta :
Answer:
The equation of circle is [tex](x-6)^{2}[/tex] + [tex](y-2)^{2}[/tex] = 153
Step-by-step explanation:
Given the endpoints of a diameter of a circle: (9,14) and (3,-10)
We know that the equation of a circle is
[tex](x-h)^{2}[/tex] + [tex](y-k)^{2}[/tex] = [tex]r^{2}[/tex]
where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.
To find (h,k): the center is midpoint of diameter
Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by
( [tex]\frac{x1+x2}{2}[/tex] , [tex]\frac{y1+y2}{2}[/tex] )
( [tex]\frac{9+3}{2}[/tex] , [tex]\frac{14-10}{2}[/tex] )
(6,2)
Hence (h,k) is (6,2)
Substituting values of (h.k) and (x.y) as (6,2) and (9,14) respectively in equation of circle, we get
[tex](9-6)^{2}[/tex] + [tex](14-2)^{2}[/tex] = [tex]r^{2}[/tex]
[tex]r^{2}[/tex] = 153
Substituting the values of (h,K) and [tex]r^{2}[/tex], we get the equation of circle as
[tex](x-6)^{2}[/tex] + [tex](y-2)^{2}[/tex] = 153
Hence the equation of circle is [tex](x-6)^{2}[/tex] + [tex](y-2)^{2}[/tex] = 153
