SOLUTION: Sketch the graph and identify focus, directrix, vertex, latus rectum and axis of symmetry: x^2 = 18y Thank you very much!

Algebra ->  Linear-equations -> SOLUTION: Sketch the graph and identify focus, directrix, vertex, latus rectum and axis of symmetry: x^2 = 18y Thank you very much!       Log On


   



Question 1087425: Sketch the graph and identify focus, directrix, vertex, latus rectum and axis of symmetry: x^2 = 18y
Thank you very much!

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
This one is similar to the other ones I did for you except that
y and x are interchanged, h and k are interchanged, graphs opening 
right and left are changed to opening up and down.

%28x-h%29%5E2=4p%28y-k%29

has vertex (h,k), and distance from vertex to both focus
and directrix is |p|.  If p is positive the parabola opens
upward with the horizontal directrix is |p| units below the 
vertex and the focus is |p| units above the vertex.  

%28x-0%29%5E2=18%28y-0%29

has vertex (0,0), and distance from vertex to both focus
and directrix is |18/4| or 9/2.  Since 9/2 is positive the 
parabola opens upward with the vertical directrix 9/2 units  
below the vertex and the focus is 9/2 above the vertex.  

So the focus is 9/2 units above vertex (0,0) which is (0,9/2),
and the directrix is a horizontal line 9/2 units below the 
vertex (0,0) which is the horizontal line y = -9/2



Edwin