Question

Find the standard form of the equation of the circle with endpoints of a diameter at the points (3,4) and (-9,6).

Answer 1

Answer:

• (x + 3)² + (y - 5)² = 37

Step-by-step explanation:

The center is the midpoint of the diameter, the coordinates are:

• x(M) = (3 - 9)/2 = -3
• y(M) = (4 + 6)/2 = 5

The length of the diameter:

• $d = \sqrt{(-9-3)^2+(6-4)^2} = \sqrt{12^2+2^2} = \sqrt{148} = 2\sqrt{37}$

The radius is:

• r = d/2 = $2\sqrt{37} /2 = \sqrt{37}$

The standard form is:

• (x - h)² + (y - k)² = r², where (h, k) is the center

Substitute to get:

• (x - (-3))² + (y - 5)² = (√37)²
• (x + 3)² + (y - 5)² = 37