Question

Write the equation of the circle containing the points J(-3, -3), K(1, -3), and L(1, 1). Show all work to receive credit.

Answer 1

Set up a system of equations.
(-3 - h)^2 + (-3 - k)^2 = r^2
(1 - h)^2 + (-3 - k)^2 = r^2
(1 - h)^2 + (1 - k)^2 = r^2

Start with the first two:
(-3 - h)^2 + (-3 - k)^2 = r^2
-1((1 - h)^2 + (-3 - k)^2 = r^2)

(-3 - h)^2 + (-3 - k)^2 = r^2
-(1 - h)^2 - (-3 - k)^2 = -r^2

(-3 - h)^2 - (1 - h)^2 = 0
9 + 6h + h^2 - (1 - 2h + h^2) = 0
9 + 6h + h^2 - 1 + 2h - h^2 = 0
8h + 8 = 0
h = -1

Now go into the second pair of equations:
(1 - h)^2 + (-3 - k)^2 = r^2
-1((1 - h)^2 + (1 - k)^2 = r^2)

(1 - h)^2 + (-3 - k)^2 = r^2
-(1 - h)^2 - (1 - k)^2 = -r^2

(-3 - k)^2 - (1 - k)^2 = 0
9 + 6k + k^2 - (1 - 2k + k^2) = 0
9 + 6k + k^2 - 1 + 2k - k^2 = 0
8k + 8 = 0
k = -1
Use the distance formula.
Center: (-1, -1)
r = 2√2
Rewrite the formula
(x - h)^2 + (y - k)^2 = r^2
(x - (-1))^2 + (y - (-1))^2 = 2√2^2
(x + 1)^2 + (y + 1)^2 = 8

Answer 2

Man. That took forever!
It should take less time when not showing every little step. :)

Answer 3

ok. wow. thank you so much. I had no idea what i was doing. this helps alot!

Answer 4

You're welcome :)

Answer 5

:) i just did that for another problem; glad to see i was in the right track tho