How do use the method of translation of axes to sketch the curve x^2-y^2+4x-2y+2=0?

1 Answer
Jan 19, 2017

X^2 - Y^2 = 1

Explanation:

Begin by completing the square

x^2-y^2+4x-2y+2=0

(x^2 + 4x) -(y^2+2y)+2=0

((x +2)^2 - 4) -((y+1)^2-1) +2=0

(x +2)^2 - 4 - (y+1)^2 + 1 +2=0

implies (x +2)^2 - (y+1)^2 = 1

IOW a hyperbola based around (-2,-1)

Or in our new co-ordinate system where X = x+ 2, Y = y + 1

implies X^2 - Y^2 = 1