the equation of a circle with endpoints of the diameter at (2, -5) and (-4, 3).?

Answer 1

Centre (-1,-1)
r² = (- 4 + 1)² + (3 + 1)²
r² = 9 + 16
r² = 25
(x + 1)² + (y + 1)² = 25 is equation of circle.

Answer 2

The equation of the circle is

(x - a)^2 + (y - b)^2 = r^2

where (a, b) is the coordinate of the center of the circle, and r is the radius.

Now, to find the center of the circle, it is the middle of the diameter. The center coordinates are the average of the endpoints. So the average of the x coordinate is (2+ (-4))/2 = -1, and the average of the y coordinates are ((-5) + 3)/2 = -1

The radius length is half of the length of the diameter. The length of any line segment is given by the equation

Squareroot( (x2 - x1)^2 + (y2 - y1)^2)

So in this case diameter = sqrt(36 + 64) = sqrt(100) = 10

Hence, the radius = diameter/2 = 10/2 = 5

So now, lets substitute everything in the first equation up there, you get

(x + 1)^2 + (y+1)^2 = 25

as the equation for the circle u're looking for.

Answer 3

Using the Midpoint Formula, the midpoint of the line segment formed by (2,-5) and (-4, 3) is (2+-4, -5+3) or (-2, -2). The midpoint of the diameter is also the center of the circle.

The equation of a circle is (x-h)^2 + (y-k)^2=r^2 where (h,k) is the center. Plug in (-2,-2) and get:

(x+2)^2 + (y+2)^2 = 25


**the radius can be found by plugging one endpoint and the center into the distance formula, which gives you 5.