the equation $y^2=4x+4y$ changes to the form $y^2=4x$ if the origin shifted to (without rotating the axis)

Question

the equation $y^2=4x+4y$ changes to the form $y^2=4x$ if the origin shifted to (without rotating the axis)

$A:(1,2)$

$B:(-1,2)$

$C:(-1,-2)$

$D:(1,-2)$

Answer 1

Hint:

$y^2=4x+4y$ is equivalent to $(y-2)^2=4(x+1)$.

Answer 2

Fill in the blanks to by completing the square.

$y^2=4x+4y$

$y^2-4y=4x$

$y^2-4x+\color{blue}{?}=4x+\color{blue}{?}$

$(y-\color{green}{?})^2=4(x-\color{red}{?})$

$(y')^2=4x'$ where $(x',y')=(0,0)$ when $(x,y)=(\color{red}{?},\color{green}{?})$.

Answer 3

Being the lazy person I am, I just plugged in A, B, C, and D to get a feel for the problem. Then, we can take some values for $y^2=4x+4y$.

$x = -1, y = 2$

$x = 0, y = 4$

$x = 1, y \approx 4.82$

As you can see, when $x = -1$, $y = 2$. The answer choice is B.

-FruDe