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.

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.

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.

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?)

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