Math Help - circle

1. circle

hi,

write down the equation of the circle which is obtained by applying the given translation to the given circle:

$[1, 0]$ $x^2 + y^2 + 4x - 2y = 2$

i first started by rearranging the equation into:
$(x + 2)^2 - 4 + (y - 1)^2 - 1 = 2$ and then
$(x + 2)^2 + (y - 1)^2 = 7$ and then translate it
$(x + 1)^2 + (y - 1)^2 = 7$

but the books answer is $x^2 + y^2 + 2x - 2y = 5$

can someone show me the steps to arriving at that answer please and also where i went wrong with mine? thanks

2. Originally Posted by mark
hi,

write down the equation of the circle which is obtained by applying the given translation to the given circle:

$[1, 0]$ $x^2 + y^2 + 4x - 2y = 2$

i first started by rearranging the equation into:
$(x + 2)^2 - 4 + (y - 1)^2 - 1 = 2$ and then
$(x + 2)^2 + (y - 1)^2 = 7$ and then translate it
$(x + 1)^2 + (y - 1)^2 = 7$

but the books answer is $x^2 + y^2 + 2x - 2y = 5$

can someone show me the steps to arriving at that answer please and also where i went wrong with mine? thanks
$(x + 2)^2 - 4 + (y - 1)^2 - 1 = 2$ and then
$(x + 2)^2 + (y - 1)^2 = 7$ and then translate it
$(x + 1)^2 + (y - 1)^2 = 7$
just simplify the power i.e

$(x+1)^2+(y-1)^2 = 7$

$x^2+2x+1+y^2-2y+1 = 7$

$x^2+2x+y^2-2y = 7-2=5$