Expert: Sherry Wallin - 11/25/2008

Question
hey..i really needed help with how to figure out the equation of a parabola if the focus and vertex is given...and could u plz eplain the x2 = 4ay thing..and wat changes if it becomes y2=4ax??

thanku

Answer
Hi Aaminah~
    y^2=4ax is the equation of a parabola with vertex at (0,0) and focus at (a,0). The directrix is always parallel to the axis of the variable that is squared. So in y^2=4ax the directrix is parallel to the y axis and in x^2 = 4ay the directrix is parallel to the x-axis. The squared variable tells you whether the parabola is opening up/down or left/right. x^2 tells you up/down and y^2 tells you left/right. On x^2 = 4ay if a is positive the parabola opens up and if the a is negative the parabola opens down. On y^2 = 4ax if a is positive the parabola opens to the right and if a is negative then the parabola opens to the left.  In other words the first equation x2 = 4ay
gives you a parabola that is open up or down and you can picture it as moving parallel to the y-axis and the 2nd equations is a parabola that opens left/right and you can picture it as moving parallel to the real or x-axis. Does this help you and answer your question or is there more you need to know?

Math Prof
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