is the equation of the required circle.
Step-by-step explanation:
Step 1 :
Let A = (8,-9) and B = (6,-3) be the endpoints of the diameter of the given circle.
We need to determine the circle's equation with this diameter
Step 2 :
The mid point of the diameter will be center of the required circle.
Let M = (x,y) be the mid point of the circle.
So we have x = (8+6)÷ 2 , y = ((-9) + (-3)) ÷ 2
M = ( 7, -6) is the midpoint of the diameter and the center of the circle.
Step 3 :
The radius of the circle is distance between midpoint and any one of the end point of the diameter that is distance between point A(8,-9) and M ( 7,-6)
Distance between the 2 points
is given by
![\sqrt{(x_{2}-x_{1})^{2}+ (y_{2}-y_{1})^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%20%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%20%7D)
So distance between A(8,-9) and M ( 7,-6) = ![\sqrt{(7-8)^{2}+ (-6-(-9))^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%287-8%29%5E%7B2%7D%2B%20%28-6-%28-9%29%29%5E%7B2%7D%20%7D)
= ![\sqrt{(1)^{2}+ (3)^{2} } = \sqrt{10 }](https://tex.z-dn.net/?f=%5Csqrt%7B%281%29%5E%7B2%7D%2B%20%283%29%5E%7B2%7D%20%7D%20%3D%20%20%5Csqrt%7B10%20%7D)
Hence the radius r is ![\sqrt{10}](https://tex.z-dn.net/?f=%5Csqrt%7B10%7D)
Step 4 :
The equation of circle with center (a,b) = (7,-6) and radius r =
is given by
![(x-a)^{2} + (y-b)^{2} = r^{2}](https://tex.z-dn.net/?f=%28x-a%29%5E%7B2%7D%20%20%2B%20%28y-b%29%5E%7B2%7D%20%3D%20r%5E%7B2%7D)
=>
=>
is equation of the required circle.
Step 5 :
Answer :
is equation of the required circle.