1. ## circle

hi,

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

$\displaystyle [1, 0]$$\displaystyle x^2 + y^2 + 4x - 2y = 2 i first started by rearranging the equation into: \displaystyle (x + 2)^2 - 4 + (y - 1)^2 - 1 = 2 and then \displaystyle (x + 2)^2 + (y - 1)^2 = 7 and then translate it \displaystyle (x + 1)^2 + (y - 1)^2 = 7 but the books answer is \displaystyle x^2 + y^2 + 2x - 2y = 5 can someone show me the steps to arriving at that answer please and also where i went wrong with mine? thanks 2. Originally Posted by mark hi, write down the equation of the circle which is obtained by applying the given translation to the given circle: \displaystyle [1, 0]$$\displaystyle x^2 + y^2 + 4x - 2y = 2$

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

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

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

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

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

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