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

Question

Write the equation of a circle with endpoints of the diameter at (2, -5) and (-4, 3).
Show your work for credit.

Thanks, I looked into the lesson, and i cant figure this out, every time i follow the formula, I seem to get it wrong, Please help with this one. I would really appreciate it!

Thanks To All!

Answer 1

The equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) are the coordinates of the center.

First you must find the center of the circle by finding the slope of the line between the two endpoints. That is, -4-2=-6 and 3-(-5)=-8. (This can also be seen as (2,-5) being 6 in front of and 8 below (-4,3).) So if you take half of -6 and -8 (ie -3, -4) then add this to (-4,3) you see the center is at (-1, -1). This will be your (h,k) values. If you are confused, try graphing the points and you will see it.

The next step is to find the radius. Since the two points are not in a straight line, you must use the pythagorean theorem, that is, you find the values of the two sides, a and b, to derive the value of the diagonal, c: a^2+b^2=c^2. Since we alread know the sides of the diameter, let's use those and then divide the answer for c by two to find the radius.

(-6)^2+(-8)^2=c^2 => 36+64=c^2 => 100=c^2 => sqrt(100)=c^2 => c=10

This is the length of the diameter, so divide by two to get the radius, r=5.

Now plug (h,k) and r into the equation for a circle:

(x-(-1))^2 + (y-(-1))^2 = 5^2
or
(x+1)^2 + (y+1)^2 = 25

Answer 2

The trick is to first find the center of the circle. The center would be halfway between the points (2,-5) and (-4,3).
To find the center, you take the average x value and the average y value:
x = (2-4)/2 = -1
y = (3-5)/2 = -1
So the center of the circle is (-1,-1).
Now you have to find the diameter. This is the distance between the center and one of the points on the circle. So let's take the distance between (-1,-1) and (2,-5).
distance = sqrt((-1-2)^2 + (-1+5)^2) = sqrt(9+16) = sqrt(25) = 5.
So the radius of the circle is 5.

Now, using the equations of a circle: (x-a)^2 + (y-b)^2 = r^2 where (a,b) is the center and r is the radius, you get:
(x+1)^2 + (y+1)^2 = 25

Good luck!

Answer 3

If P (x,y ) is a point of the circle and A andBthe given end points
AP and BP are perpendicular so the product of their slopes is -1
(y+5)/(x-2) *(y-3)/(x+4) =-1
so (x-2)(x+4) +(y+5)((y-3)=0
x^2 +y^2 +2x +2y-23=0

Answer 4

the radius is the distance from 2 points
r= sqrt( [2- -4]^2 + [-5-3]^2)
r=sqrt(6^2+(-8)^2)
r=sqrt(36+64)= sqrt 100 = 10
the center is depend on you , you can pick the point (2, -5)
equation is some like (x-h)^2+(y-k)^= r^2
(x-2)^2+(y--5)^2=100
(x-2)^2+(y+5)^2=100