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Find the standard form of the equation of the parabola with a focus at (3, 0) and a directrix at x = -3.

Ay = (1/12)x^2
B-12y = x^2
Cx = (1/12)y^2
Dy^2 = 6x

Verified Answer :

notice the picture below

the directrix is a vertical line, and the focus point is to the right of it
the vertex is always half-way between those two, at h,k coordinates

thus the parabola is opening sideways, to the right, thus the "y" is the
variable that's at the second power

or \(\bf \begin{array}{llll} \boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\ (x-{{ h}})^2=4{{ p}}(y-{{ k}})\\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\)

so... use those values, and plug them in the equation

View image jdoe0001

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