Problem 83 - College Algebra and Calculus: An Applied Approach

Question

Find the center and radius of the circle given the endpoints of the diameter of the circle.

Step-by-Step Solution

Answer

The center of the circle is given by the coordinates (h, k) and the radius by r.

Step 1: Identify the coordinates

Let's denote the endpoints of the diameter as A(x1, y1) and B(x2, y2).

Step 2: Find the center of the circle

You can find the center (h, k) of the circle by using the midpoint formula. Thus, h = (x1 + x2)/2, k = (y1 + y2)/2. Substitute the given coordinates into the formula and calculate the center.

Step 3: Calculate the distance between the center and one end

You can calculate the radius of the circle (r) using the distance formula, which is r = sqrt[(x2-h)² + (y2-k)²]. Substitute the coordinates of the center and one endpoint into the formula, then calculate the radius.