Is this equation a ellipse, circle, hyperbola or parabola:
x^2-10x+25=y and why?

Question

Is this equation a ellipse, circle, hyperbola or parabola: 
x^2-10x+25=y and why?

turingtest · Answer

x^2-10x+25=y
can be factored into
y=(x-5)^2
which is a parabola with vertex (5,0)

anonymous · Answer

I thought a parobla had to be in the form of someting like 1/80y^2=x

anonymous · Answer

i hope this would help http://higheredbcs.wiley.com/legacy/college/anton/0471472441/appendices/apph.pdf

turingtest · Answer

do you recognize that 
y=x^2 is a parabola?

anonymous · Answer

yes

turingtest · Answer

then look for something like
(y-b)=(x-a)^2
Realize the similarity in forms, the only difference is that this parabola will have a vertex at (a,b). if we let a=0 and b=0, the above becomes
y=x^2
which, as you know, is a parabola at vertex (0,0)

anonymous · Answer

i know that..i'm just suggesting a general method to determine the kind of conic section..
using the discriminant method, any equation of a conic section will be identified instantly..

turingtest · Answer

Oh, @kelu I thought I was talking to Cooper. But even so I think the page you linked for him is beyond most algebra students.