Answer:
The equation is (x+9)^2 + (y-3)^2 = 5
Explanation:
The standard form for the equation of a circle is:
(x−h)^2+(y−k)^2=r2
The center of the circle is the midpoint of the diameter.
So the midpoint of the diameter at (-10, 1) and (-8, 5) can be determined as:
(-10 +(-8))/2 , (1+5)/2
= -10-8/2, 1+5/2
= -18/2 , 6/2
= -9 , 3
Thus(-9,3) is the center of the circle.
Now we will use the distance formula to find the radius of the circle.
r^2=(-10-(-9))^2 + (1-3)^2
r^2=(-10+9)^2 +(-2)^2
r^2=(-1)^2 + (-2)^2
r^2=1 + 4
r^2= 5
Take square root at both sides.
√r^2= √5
r=√5
Now put the values in the 1st equation.
(x−h)^2+(y−k)^2=r2
where h = -9, k =3 and r = √5
(x-(-9))^2 + (y-3)^2= (√5)^2
(x+9)^2 + (y-3)^2 = 5
Thus the equation is (x+9)^2 + (y-3)^2 = 5 ....