how to find focus of y^2=2x?
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 $\displaystyle \subset$
. . . . $\displaystyle \text{depending on the sign of }p.$
. . $\displaystyle \text{Its Vertex is at the Origin.}$
. . $\displaystyle p\text{ is the directed distance from the Vertex to the Focus.}$
$\displaystyle \text{Your equation has: }\:4p \,=\,2 \quad\Rightarrow\quad p \:=\:+\tfrac{1}{2}$
$\displaystyle \text}This parabola has its vertex at the Origin: }\,V(0,0)$
. . $\displaystyle \text{and opens to the right: }\,\subset$
$\displaystyle \text{The Focus is }\tfrac{1}{2}\text{ unit to the }right\text{ of the Vertex: }\:F\left(\tfrac{1}{2},\,0\right)$
Thank you SOROBON.your explanation is really good and easily understandable.
Thank you
Bizworldusa