Question

Find the equation of a circle that has a diameter with endpoints at (0, 4) and (-3, 1) then tell me how you did it :)

Use algebra.

Answer 1

centre is mid point of diameter
(0,4) (-3,1) midpoint [(0 +-3)/2 , (4+1)/2]
Midpoint = centre of circle = [ -1.5, 2.5]
Radius is half of diameter
Length of diameter = sqrt( 18) = 3 sqrt(2)
Radius = 3sqrt(2) / 2
Use these to find the equation of circle

Answer 2

i did use algebra ...

http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e5c4f2f0b8b1f45b48adb9c

Answer 3

General equation of a circle is \[\large (x-h)^2+(y-k)^2=r^2\] where (h,k) is the center and 'r' is the radius


So we need the center point and the value of r


To find the center, simply find the midpoint of the diameter (just average the corresponding coordinates)


To find the radius, first find the length of the diameter, which amounts to finding the distance between the two points. The radius will be equal to half of the diameter.

Answer 4

im old, so i tend to use the algebra in steps instead of cramming it all into one compact formula ... thats all :)

Answer 5

thanks Aimistre, and you jim. (and you rita)

Answer 6

Oh hold up, I don't get how you found the diameter :(

Answer 7

find the distance between the two points to find the length of the diameter

Answer 8

d = sqrt((x2-x1)^2+(y2-y1)^2)



d = sqrt((-3-0)^2+( 1- 4)^2)



d = sqrt((-3)^2+(-3)^2)



d = sqrt(9+9)



d = sqrt(18)



d = 3*sqrt(2)



So exact distance between the two points is 3*sqrt(2) units.


Do the diameter is exactly 3*sqrt(2) units long

Answer 9

oops *So the diameter is exactly 3*sqrt(2) units long lol

Answer 10

yeah I just looked up the distace formula.

Answer 11

but thank you!

Answer 12

yeah, the distance for diameter is just using the pythag thrm once you determine the x and y distances; which is why i subtract the points to find the distances:

(0,4)
-(-3,1)
-------
3, 3

sqrt(3^2 + 3^2) = sqrt(18) = 3sqrt(2) right?

Answer 13

the distance formula says:

\[d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\]
which is to say, subtract the points and pythag the results