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

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Answer 1 · 2017-01-19T14:56:32

# X^2 - Y^2 = 1#

#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#