Q:

# 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 ?

Accepted Solution

A:
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