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Flapdragon
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?
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
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
seems to be a problem with the centre, in particular the y value
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 ?
Thank you! c: It's fine.
glad to help <tips hat>
myplesure og helping u
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