Write the equation of a circle whose diameter has endpoints (2, 7) and (4, -3).Question 9

The equation of a circle is given by (x-h)² + (y-k)² = r² where (h,k) is the center of the circle and r is the radius.

Step 1: Find the center of the circle The center of the circle is the midpoint of the diameter. The midpoint is given by the average of the x-coordinates and the y-coordinates of the endpoints.

So, h = (2+4)/2 = 3 and k = (7-3)/2 = 2. Therefore, the center of the circle is (3,2).

Step 2: Find the radius of the circle The radius of the circle is half the length of the diameter. The length of the diameter is the distance between the endpoints, which can be found using the distance formula: sqrt[(x2-x1)² + (y2-y1)²].

So, r = sqrt[(4-2)² + (-3-7)²]/2 = sqrt[4 + 100]/2 = sqrt[104]/2 = sqrt[26].

Step 3: Write the equation of the circle Substitute h, k and r into the equation of the circle to get the final equation.

So, the equation of the circle is (x-3)² + (y-2)² = 26.