# Thread: Locus focus question help! :)

1. ## Locus focus question help! :)

how to find focus of y^2=2x?

2. ## Re: Locus focus question help! :)

Perhaps: $\displaystyle y=\pm \sqrt{2x}$

3. ## Re: Locus focus question help! :)

Hello, navkay96!

$\displaystyle \text{Find the focus of: }\:y^2\:=\:2x$

$\displaystyle \text{You are expected to know the following . . .}$

$\displaystyle \text{The graph of }y^2 \,=\,4px\text{ is a "horizontal" parabola.}$
. . $\displaystyle \text{It opens to the left or right: }\,\supset$ or $\displaystyle \subset$
. . . . $\displaystyle \text{depending on the sign of }p.$
. . $\displaystyle \text{Its Vertex is at the Origin.}$
. . $\displaystyle p\text{ is the directed distance from the Vertex to the Focus.}$

$\displaystyle \text{Your equation has: }\:4p \,=\,2 \quad\Rightarrow\quad p \:=\:+\tfrac{1}{2}$

$\displaystyle \text}This parabola has its vertex at the Origin: }\,V(0,0)$
. . $\displaystyle \text{and opens to the right: }\,\subset$

$\displaystyle \text{The Focus is }\tfrac{1}{2}\text{ unit to the }right\text{ of the Vertex: }\:F\left(\tfrac{1}{2},\,0\right)$

4. ## Re: Locus focus question help! :)

Thank you SOROBON.your explanation is really good and easily understandable.
Thank you
Bizworldusa