College algebra

Question

Find the standard form for the equation of a circle 

(x−h)squared + (y−k)squared = r2

with a diameter that has endpoints (−2,2) and (3,8)

h=

k=

r=

Answer 1

Hello, thank you for taking the time to post your question!

You can use the two endpoints in order to find both the center of the circle (h,k) and the radius of the circle.

For the center you want to find the midpoint between the two endpoints

(h,k) = ( (x1 + x2)/2, (y1 + y2)/2 ) = ((-2 + 3)/2 , (2 + 8)/2) = (1/2, 5)

For the radius then you want to find the distance from the center point of (1/2, 5) to one of the end points … I would use (3,8) and the distance formula to find that!

r = sqrt((3 – ½)^2 + (8 – 5)^2)) = sqrt(61/4)

putting it all together in standard form then is

(x – ½)^2 + (y-5)^2 = 61/4

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

(3,8) and (-2,2) as "endpoints" means the circle's middle is their midpoint. Take the average of the x and y coordinates: 3--2 = 5, 5/2 = 2.5. Add 2.5 to -2 to get 1/2 for the x coordinate of the center. 8-2 = 6. 6/2 =3. add 3 to 2 to get 5 as the y coordinate of the center. Circle's center is (1/2, 5)

the radius is the distance from the center to either endpoint: 2.5

the circle's equation is (x-1/2)^2 + (y-5)^2 = 15.25

h=1/2

k= 5

r = sqr(15.25)