## Flapdragon 2 years ago 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?

1. Rohangrr

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

2. lgbasallote

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

3. campbell_st

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

4. lgbasallote

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 ?

5. Flapdragon

Thank you! c: It's fine.

6. lgbasallote

7. Rohangrr

myplesure og helping u

8. campbell_st

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