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Question 554723: I do not need help on a specific problem; however, I would appreciate guidance on how to do a few problems. It is called "Analyzing a Parabola" in my book. I am to find the vertex, focus, and directrix of the parabola. My book tells me to "complete the square," but I've never seen this specific type of equation that required completing the square. Here is an example of one: y^2-25x=0 . I do not even know where to start, but I did try to solve for y; however, I got stuck on y^2=25x. I would really appreciate if you could help me because I could use some guidance. Thank you for your time.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! y^2-25x=0
y^2=25x
This is an equation of a parabola of the standard form: (y-k)^=4p(x-h), with (h,k) being the (x,y) coordinates of the vertex.
For given equation: y^2=25x
Vertex: (0,0)
axis of symmetry: x-axis or y=0 (parabola opens rightward)
4p=25
p=25/4=6.25
focus=(p,0)=(6.25,0)
directrix: x=-6.25 (p distance from vertex on the axis of symmetry)
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