189k views
3 votes
A diameter of a circle has endpoints A(-4,2) and B(3,2). Find the center of the circle, radius, and write an equation for the circle. * 0 points

1 Answer

4 votes
The center of a circle is the midpoint of its diameter. To find the midpoint of AB, we add the x-coordinates of A and B and divide by 2, and add the y-coordinates of A and B and divide by 2:

Midpoint = ((-4 + 3)/2, (2 + 2)/2) = (-0.5, 2)

So the center of the circle is at (-0.5, 2).

The radius of the circle is half the length of the diameter. To find the length of AB, we use the distance formula:

AB = sqrt((3 - (-4))^2 + (2 - 2)^2) = sqrt(49) = 7

So the radius of the circle is 7/2.

The equation for a circle with center (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

Plugging in the values we found, we get:

(x - (-0.5))^2 + (y - 2)^2 = (7/2)^2

Simplifying, we get:

(x + 0.5)^2 + (y - 2)^2 = 49/4

Therefore, the equation for the circle is (x + 0.5)^2 + (y - 2)^2 = 49/4.
User Svek
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories