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