SOLUTION: Find the coordinates of the focus and the vertex, the equations of the directrix and the axis of symmetry, and the direction of opening of the parabola. y^2 - 12x = 0 -------

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the coordinates of the focus and the vertex, the equations of the directrix and the axis of symmetry, and the direction of opening of the parabola. y^2 - 12x = 0 -------      Log On


   

Question 1204729: Find the coordinates of the focus and the vertex, the equations of the directrix and the axis of symmetry, and the direction of opening of the parabola.
y^2 - 12x = 0
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This to me looks like a completing the square type problem, but I don't know how to complete a square with only two terms like these.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!




y%5E2+-+12x+=+0
y%5E2+=12x+
vertex form of your parabola is:
%28y+-+k%29%5E2+=+4a%28x+-+h%29 where (h, k) is vertex and (h+%2B+a, k) is focus
your parabola in vertex form will be:
%28y+-+0%29%5E2+=+12%28x+-+0%29
as you can see, h=0, k=0, 4a=12 =>+a=3
vertex is at origin (0,0)
focus is at (0+%2Ba, 0)= (0+%2B3, 0)=(3,0)
the axis of symmetry is y=k+=>+y=0
The focus and the directrix lie on either sides of vertex of the parabola and are equidistant from the vertex.
so, x=-a+and the equations of the directrix is+x=-3+