I just want to check if my answer is correct.
The problem is: Find the center of the circle passing through (9,-2),(2,5),(-3,6).
My answer is: (-3,-7)
That's correct!!
Plug each point into the center-radius equation, since each radius will have the same center point
(h, k), and radius, r
(9, - 2)
------- eq (i)
(2, 5)
------- eq (ii)
(- 3, 6)
------- eq (iii)
------- eq (i)
------ eq (ii)
– 14h + 14k = - 56 ------ Subtracting eq (ii) from eq (i)
– 14(h - k) = - 14(4)
h - k = 4 ----------- eq (iv)
------ eq (ii)
------ eq (iii)
– 10h + 2k = 16 ------ Subtracting eq (iii) from eq (ii)
- 2(5h - k) = - 2(- 8)
5h - k = - 8 --------- eq (v)
h - k = 4 -------- eq (iv)
5h - k = - 8 -------- eq (v)
- 4h = 12 -------- Subtracting eq (v) from eq (iv)
, or – 3
- 3 - k = 4 ----- Substituting - 3 for h in eq (iv)
- k = 4 + 3
– k = 7
, or - 7
With h = - 3, and k = - 7, center coordinate point (h, k) is: