the equation $y^2=4x+4y$ changes to the form $y^2=4x$ if the origin shifted to (without rotating the axis)
$A:(1,2)$
$B:(-1,2)$
$C:(-1,-2)$
$D:(1,-2)$
$\endgroup$ 23 Answers
$\begingroup$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
$\endgroup$ $\begingroup$Hint:
$y^2=4x+4y$ is equivalent to $(y-2)^2=4(x+1)$.
$\endgroup$ 3 $\begingroup$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 $(x,y)=(\color{red}{?},\color{green}{?})$.
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