SOLUTION: Write the equation of the parabola with given vertex at the origin and directrix: 3x=-4

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Question 982925: Write the equation of the parabola with given vertex at the origin and directrix: 3x=-4
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The directrix given can be expressed x=-4%2F3, and y is unrestricted. This parabola has axis of symmetry being the x-axis, and since this directrix is to the left of the vertex(the origin), the parabola is concave to the right.

Using the equation of form which comes from deriving from the definition of a parabola, 4py=x%5E2, and because the distance from your directrix and the vertex is abs%28-4%2F3%29=4%2F3, this determines highlight_green%28p=4%2F3%29.

Substitute for p into the derived equation form.
4%284%2F3%29x=y%5E2

Simplifiable to highlight%28%2816%2F3%29x=y%5E2%29

You can also derive the equation for your description using your given directrix x=-4%2F3 and the focus 4/3 units to the right of the vertex ; the focus which is ( 4/3, 0), using the definition and Distance Formula.