Hello Omar,
First, you need to recall the formula for the equation of a circle:
(x – h)2 + (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius
You're given 2 endpoints on the circle; you can use those to find center of the circle by applying the midpoint formula.
xM = (-1+7)/2 = 6/2 = 3
yM = (-3+3)/2 = 0/2 = 0
Therefore, the center of the circle has coordinates (3,0) so you can replace h & k in the circle equation by 3 and 0 respectively: (x – 3)2 + (y – 0)2 = r2
You can find the radius by replacing x and y by the coordinates of one of the 2 endpoints (doesn't matter which), let's take the first one, (-1,-3):
(-1 – 3)2 + (-3 – 0)2 = r2
(-4)2 + (-3 )2 = r2
16 + 9 = r2 ---> 25 = r2 ----> r = 5
Your complete circle equation is then: (x – 3)2 + (y)2 = 25
Knowing the radius, you can replace x and y by 0 and b, then solve for b.
(0 – 3)2 + (b)2 = 25
(– 3)2 + b2 = 25 ------> 9 + b2 = 25 ---> b2 = 16
The question mentions that b> 0 , that means b = 4
The value of b is 4.
Cheers.
