write an equation for a circle if the endpoints of a diameter are at (1,1)and (1, -9)?

Question

a. (x-1)^2+(y+4)^2=5
b. (x-1)^2+(y+4)^2=25
c. (x+1)^2+(y-4)^2=5
d. (x+1)^2+(y-4)^2=25

Answer 1

The general equation for a circle is (x-h)^2 + (y-k)^2 = r^2 when (h,k) is the center and r is the length of the radius.

Since the points (1,1) and (1,-9) are the endpoints of your diameter, then the diameter is 10 units long [1- -9=10]. The radius is half the diameter, so r = 5.

Since your center is going to be inbetween the endpoints, it will be at the point (1,-4). Make sure when you choose the right equation that you remember to look for the opposite of these numbers though, since the formula is (x-h) and (y-k).

Answer 2

diameter = distance between the endpoints of the diameter. √[ (-9-1)² + (1-1)² ]
d = √(-10)²
d = 10
r = 5

Center = midpoint of diameter. [ (1+1)/2,(-9+1)/2 ]
C = (1,-4)

equation = (x-1)² + (y+4)² = 25
B.

Answer 3

the answer is B. plug in either set of coordiinates to for each equation until you find the one that is correct.