Find an equation of a circle for which the endpoints of a diameter are (-5,3) and (7,-1)?

Question

a. (x-1)^2 + (y-1)^2=40
b.(x-1)^2+(y-1)^2=40
c.(x-1^2+(y-1)^2=20
d.(x-1)^2+(y-1)^2=2 squareroot 10

Answer 1

The midpoint of the endpoints of the diameter is the center of the circle. To find midpoint, just average the x's and the y's: (1, 1). So you have almost all the input you need for your circle except r:



(x-1)^2 + (Y-1)^2 = r^2



Plug in either of the two points given to you since they both lie on the circle. Any point that lies on the circle can be subbed in for x and y to find R^2. I choose (7,-1)...



(7-1)^2 + (-1-1)^2 = 36 + 4 = 40. This is R^2. Looks like your answers A or B are both right.

Answer 2

Jen, Remember that the equation of a circle is: (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and "r" is the radius. You are given the endpoints of a diameter. We can use the midpoint theorem to find the midpoint between these two points, which is the center. Xmidpoint = (7+1)/2 = 4 Ymidpoint = (-4+10)/2 = 3 So the center is at (4,3) So far our equation is: (x-4)^2 + (y-3)^2 = r^2 We still need the radius. You can find it using the distance formula with the given points and dividing by two (half the diameter), or by using one of the given points and the center that we just found. I'll do the latter. D = sqrt((7-4)^2+(-4-3)^2) D = sqrt(9+49) D = sqrt(58) Unless they are asking use for the radius, we don't need to evaluate the square root and we can write directly: (x-4)^2 + (y-3)^2 = 58 Hope this helps. -Nick

Answer 3

The answer is a or b, since they are both correct..

(There is probably a mistake in the possible answers!)

Since the point (-5,3) is on the circle, it must satisfy the equation. So just plug in -5 for "x" and 3 for "y", And since you get 40, this eliminates answers "c" and "d." The same is true for the point (7, -1).



It takes some work to actually solve this problem.

One way is to first find the center of the circle by using the midpoint formula. This comes out to (1,1). The equation of any circle is (x-h)^2 + (y-k)^2=r^2, where (h,k) is the center point, and "r" is the radius of the circle. Now we need to find the radius. Using the distance formula with the two points (1,1) which is the center, and (7,-1), we get "r"=squareroot of 40. By plugging in the center point (1,1) and the radius (squareroot of 40), the equation is now (x-1)^2 + (y-1)^2 = (root 40)^2. Thus "a" or "b" is the correct answer.

Answer 4

Answers a and b appear to be the same. Have you made a mistake in copying the question? The answer should be

(x-1)^2 + (y-1)^2 =40.

If you require an explanation then rewrite the question and I will show the working

Answer 5

are you sure you options: a,b,c,d.....are correct?

a & b are the same.

Anyway....find your distance between point (-5,3) and (7,-1), by using the distance formula, then divide by 2 to find your radius, then square it for your answer after the " = " sign. (i.e., if your radius is 6, then the answer after the = sign is 36).

Also when you graph those given points and draw a circle around them, the center of the circle will be in Quadrant I, therefore your equation will be (x-?)^2 + (y-?)^2 , {not (x+?)^2 or (y+?)^2}.