SOLUTION: find the focus and directrix of the parabola y^2=14x and sketch

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Question 1087501: find the focus and directrix of the parabola y^2=14x and sketch
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

the parabola is sideways parabola opens towards positives
or
standard formula is: where and are coordinates of vertex
in your , and
the focus is at
(, )
=(, )
=(, )
=(, )
the vertex is exactly midway between the directrix and the focus, so directrix is

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


has vertex (h,k), and distance from vertex to both focus
and directrix is |p|.  If p is positive the parabola opens
right with the vertical directrix is |p| units left of the 
vertex and the focus is |p| units right of the vertex.  



has vertex (0,0), and distance from vertex to both focus
and directrix is |14/4| or 7/2.  Since 7/2 is positive the 
parabola opens right with the vertical directrix 7/2 units  
left of the vertex and the focus is 7/2 right of the vertex.  

So the focus is 4 units right of vertex (0,0) which is (4,0),
and the dirctrix is a vertical line 7/2 units left of the 
vertex (0,0) which is the vertical line x = -7/2



Edwin
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