Question

A circle in the xy-plane has a diameter with endpoints whose coordinates are negative 1 comma negative 3 and 7 comma 3. if the point with coordinates 0 comma b lies on the circle and b is greater than 0, what is the value of b ?

Answer 1

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