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Thread: Locus focus question help! :)

  1. #1
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    Locus focus question help! :)

    how to find focus of y^2=2x?
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  2. #2
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Locus focus question help! :)

    Perhaps: $\displaystyle y=\pm \sqrt{2x}$
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  3. #3
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    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 $\displaystyle \subset$
    . . . . $\displaystyle \text{depending on the sign of }p.$
    . . $\displaystyle \text{Its Vertex is at the Origin.}$
    . . $\displaystyle p\text{ is the directed distance from the Vertex to the Focus.}$

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

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

    $\displaystyle \text{The Focus is }\tfrac{1}{2}\text{ unit to the }right\text{ of the Vertex: }\:F\left(\tfrac{1}{2},\,0\right)$
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  4. #4
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    Re: Locus focus question help! :)

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