SOLUTION: 3y2 = 24x (three y square = 24x) please help me know What is the vertex, focus, directrix and axis of symmetry of this equation of a PARABOLA?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 3y2 = 24x (three y square = 24x) please help me know What is the vertex, focus, directrix and axis of symmetry of this equation of a PARABOLA?       Log On


   

Question 1059942: 3y2 = 24x (three y square = 24x) please help me know What is the vertex, focus, directrix and axis of symmetry of this equation of a PARABOLA?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
3y^2=24x

3y%5E2=24x
3%28y-0%29%5E2=24%28x-0%29

That is the form which might be arranged if deriving the equation from parabola of known focus and known directrix. Vertex would be (0,0). Axis of Symmetry would be y=0.

You want one further adjustment to YOUR equation.
%281%2F3%293%28y-0%29%5E2=%281%2F3%2924%28x-0%29
%28y-0%29%5E2=8%28x-0%29--------conforming to the format %28y-k%29%5E2=4p%28x-h%29.

The meaning of p is the distance of the vertex from either directrix or focus. Notice here that p is a POSITIVE value.

4p=8
p=2
-
This means the focus is (0,2) and the directrix is x=-2.


See here for helpful lessons on using Distance Formula for the Definition of Parabola to derive equation:

Use definition to derive parabola equations.

Same idea, different orientation