Parabola equation

Geometric formulae, word problems, theorems and proofs, etc.
Alfred
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Joined: Fri Mar 14, 2014 6:44 pm
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Parabola equation

Postby Alfred » Sun Mar 16, 2014 4:53 am

GIVEN:
coordinates of vertex: (u,v)
coordinates of a point on parabola: (d,e)

Find equation of parabola

I got:
y = [(e - v) / (d^2 + u^2 - 2du)]x^2 - (2au)x + au^2 + v

Can someone confirm? Thank you.

FWT
Posts: 123
Joined: Sat Feb 28, 2009 8:53 pm

Re: Parabola equation

Postby FWT » Sun Mar 16, 2014 4:15 pm

Alfred wrote:GIVEN: coordinates of vertex: (u,v)
coordinates of a point on parabola: (d,e)

Find equation of parabola

I didn't times it all out, but I got y = [(e-v)/(d-u)^2](x-u)^2 + v
I think mine probably ends up like yours if you do all the steps. (Do you have to do all that?)

Alfred
Posts: 17
Joined: Fri Mar 14, 2014 6:44 pm
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Re: Parabola equation

Postby Alfred » Sun Mar 16, 2014 7:31 pm

FWT wrote:I didn't times it all out, but I got y = [(e-v)/(d-u)^2](x-u)^2 + v
I think mine probably ends up like yours if you do all the steps. (Do you have to do all that?)

Ok, but a parabola equation is of this format: y = Ax2 + Bx + C

I really should have made mine clearer:
y = Ax^2 + Bx + C
where:
A = (e - v) / (d - u)^2
B = -2Au
C = Au^2 + v

So (as example): d=4, e=6, u=10, v=-5
then (as example) these 4 points (integer coordinates) are on the parabola:
(4,6), (16,6) : end points of horizontal chord length 12
(-2,39), (22,39) : end points of horizontal chord length 24

Thanks for your reply...and pointing out that d^2+u^2-2du = (d-u)^2 :wave:


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