Question

find the equation of circle passing through the points (1,5)(5,3)&(3,-1).

Answer 1

those form a triangle that i believe you would need to find the medians of, and the center of the circle is where they intersect

Answer 2

or you could try something that might be a little tricker and find a solution to equating all these to the same distance from a point

Answer 3

sqrt((x-1)^2+(y-5)^2)
sqrt((x-5)^2+(y-3)^2)
sqrt((x-3)^2+(y+1)^2)

and see if you can equate them :)

Answer 4

sqrt((x-1)^2+(y-5)^2) = sqrt((x-5)^2+(y-3)^2)
sqrt((x-5)^2+(y-3)^2) = sqrt((x-3)^2+(y+1)^2)


(x-1)^2+(y-5)^2 = (x-5)^2+(y-3)^2
(x-5)^2+(y-3)^2 = (x-3)^2+(y+1)^2


x^2 -2x + 1+ y^2 -10y + 25 = x^2 -10x + 25 + y^2 -6y + 9
x^2 -10x + 25 + y^2 -6y + 9 = x^2 -6x + 9 + y^2 +2y +1



-2x -10y + 26 = -10x -6y + 34
-10x -6y + 34 = -6x +2y +10

Answer 5

8x -4y = 8
-4x -8y = -24

Answer 6

now that should be easier for you to determine x and y with

Answer 7

and with any luck, i didnt mess it up any lol

Answer 8

amistre64 how about i apply \[x^2+y^2+2gx+2fy+c=0\] on each of them

Answer 9

give it a shot, it might work out

Answer 10

k i did and got three equations, what do i do next

Answer 11

how many unknowns? or rather, what equations did you come up with?

Answer 12

2g+10f+c=-26, 10g+6f+c=-34 and 6g-2f+c=-10

Answer 13

i guess i'll have to find g,f and c.

Answer 14

3 eqs in 3 unknowns is doable ...

Answer 15

my way got me (2,2) as a center, and if i plug in x and y into the distances i get:

(1)^2+(-3)^2 = (-3)^2+(1)^2
(-3)^2+(-1)^2 = (-1)^2+(3)^2

d^2 = 10

(x-2)^2 + (y-2)^2 = 10 might be it

Answer 16

if the given points fit as solutions; its good :)

Answer 17

dont u think i solve them simultaneously?