x^2+y^2-2X+6y+9=0 ....help I'm stumped with x and y!!! please solve by completlying the square!?

Answer 1

x^2+y^2-2X+6y+9=0

Let me first tell you, you are looking at a conic section.

x^2+y^2-2X+6y+9=0
x^2 -2x + y^2 + 6y = -9 (first, group x terms and y terms)
x^2 - 2x +1 + y^2 + 6y + 9 = -9 +1 +9 (complete the square)
(x-1)^2 + (y+3)^2 = 1 (factor x and y)

This is as far as you can go.
It is a circle of radius 1, center at (1, -3)

Answer 2

I think you want this written in the standard form right...?

x^2+y^2-6x-4y+9=0 -----> (x^2-6x+9)+(y^2-4y+4)=4

ie adding 4 on both sides

Standard Form : (x-3)^2+(y-2)^2 = 2^2

(Factorising)