First we look for the coordinates of the center of the circle. For this, we use the following formula:
((x1 + x2) / 2, (y1 + y2) / 2)
Where,
(x1, y1) = (- 1, -3)
(x2, y2) = (7, 3)
Substituting values we have:
((-1 + 7) / 2, (-3 + 3) / 2)
((6) / 2, (0) / 2)
(3, 0)
We are now looking for the diameter of the circle. For this we use the formula of distance between points:
d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
Substituting values:
d = root ((7 - (- 1)) ^ 2 + (3 - (- 3)) ^ 2)
d = 10
Then, the radius of the circle is:
r = d / 2 = 10/2
r = 5
The circle equation will be
(x-h) ^ 2 + (y-k) ^ 2 = r ^ 2
Where,
(h, k) = (3, 0)
r = 5
Substituting
(x-3) ^ 2 + (y-0) ^ 2 = 5 ^ 2
Substituting
(x, y) = (0, b)
(0-3) ^ 2 + (b-0) ^ 2 = 5 ^ 2
b = root (25-9)
b = root (16)
b = 4
Answer
the value of b is
b = 4
