Question

Find an equation of the circle whose diameter has endpoints (-1,6) and (3,4).

A) (x - 1)^2 + (y - 6)^2 = 4
B) (x + 1)^2 + (y - 6)^2 = 4
C) (x - 1)^2 + (y + 6)^2 = 4
D) (x + 1)^2 + (y + 6)^2 = 4

Answer 1

To find the equation of a circle given the endpoints of its diameter, we can use the midpoint formula and the distance formula. The center of the circle is the midpoint of the diameter, and the radius is the distance between the center and any point on the circle. Using these formulas, we can find the equation of the circle, which is (x - 1)^2 + (y - 5)^2 = 4.

Step-by-step explanation:

To find an equation of the circle whose diameter has endpoints (-1,6) and (3,4), we need to find the center point of the circle.

The center point of the circle is the midpoint of the diameter. Using the midpoint formula, we find that the center is (-1+3)/2, (6+4)/2 = 1, 5.

Now, we can use the center and one of the endpoints to find the radius. The radius is the distance between the center and any point on the circle.

Using the distance formula, we find that the radius is the square root of [(1-(-1))^2 + (5-6)^2] = 2. Therefore, the equation of the circle is (x - 1)^2 + (y - 5)^2 = 2^2, which simplifies to (x - 1)^2 + (y - 5)^2 = 4.