Question

If the diameter of a circle has endpoints P(–10, –2) and Q(4, 6), where is the center of the circle, how long is its radius, and what is the equation for the circle?

Answer 1

The center is the midpoint of a diameter so use the midpoint formula.
C = ([-10 + 4]/2, [-8 + 4]/2)
C = (-3, -2)
Then use distance formula to get the radius (use either diameter endpoint)

r = √( [4 - -3]^2 + [4 - -2]^2)
= √(7^2 + 6^2)
= √(49 + 36)
= √85

The equation of a circle with center (h,k) and radius r is (x - h)^2 + (y - k)^2 = r^2
so (x + 3)^2 + (y + 2)^2 = 85

Answer 2

the radius would be half the distance of the diameter...you do know how to do the distance formula right? do the distance formula..that's your diameter..divide it by 2 that's your radius..

as for the center..it's the midpoint of your diameter

Answer 3

seems to be a problem with the centre, in particular the y value

Answer 4

the equation of the circle is just combine all the gathered information from the coordinates of the center and the length of the radius...do you need further hints? @Flapdragon ?

Answer 5

Thank you! c: It's fine.

Answer 6

glad to help <tips hat>

Answer 7

myplesure og helping u

Answer 8

I think the centre is x (-10 + 4)/2 = -3 y = (-2 + 6)/2 = 2

centre is (-3, 2)

radius = \[\sqrt{(-10 +3)^2 (-2 -2)^2} = \sqrt{49 + 16} = \sqrt{65}\]

so the equation of the circle is

(x +3)^2 + (y -2)^2 = 65