# My solution is right and the book is wrong (parabolas) or did I misunderstand it?

Find the equation of the parabola with the vertex at the origin; directrix 2x = 3

So what I did is, find the equation of the directrix $$x = \frac{3}{2}$$ and then because its the directrix, the focus must be $$\bigl(-\frac{3}{2},0\bigr)$$ then multiplying it by 4, I get the equation $$y^2 = -6x$$ I'm correct right? because the book said the answer is $3y^2 = -8x$ and I've checked using graphing softwares that it isn't the same graph as my answer. Graphing softwares don't show the directrix so I can't confirm it. Although I've checked my answer and it seems odd that our textbook is wrong this time.

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The equation of a parabola that opens left/right with vertex at the origin and directrix $x=-p$ is $y^2=4px$. Here, you have $p=-3/2$. So, you're right. It seems the book made an error in division, somehow obtaining $x=2/3$ from $2x=3$... – David Mitra Jan 14 '13 at 15:22
@DavidMitra Would you mind putting a version of that comment as an answer so this no longer stays unanswered? If you would mind, perhaps goldencalf should do it. – Mark S. Jan 1 '14 at 3:50

The book is wrong, you are right. The left opening mouth parabola is $y^2 = - 4 f x$, so focal length $f = - \frac32$ to the left from origin and directrix $f = x= + \frac32$ to the right.