Parametrics (2 Viewers)

[toodaloo]

If you have an equation: x^2 = -4y, is a = -1 or a=1??
im so confused...

 

[xV1P3R]

a=-1, because you the parabola is in the form x² = 4ay
Equating it to your equation, you get a = -1

It's just the normal parabola, flipped along the x-axis

 

[xV1P3R]

I thought focal length would be |a| as opposed to a.

 

[yugi]

yeah i dont get this either
what wuold teh answer be if you had to write down the parametric equation for the parabola
x^2=-4y

would it be
a=-1
x=-2t, y =-t^2?

 

[alchetor]

yeah i dont get this either
what wuold teh answer be if you had to write down the parametric equation for the parabola
x^2=-4y

would it be
a=-1
x=-2t, y =-t^2?

a=1 , as a=length and hence a>0,
and then your parametric equations are correct
note: as the form x=+2at , y= +at^2 is for the parabola x^2 = 4ay
and x=-2at, y=-at^2 for x^2 = -4ay(remembering that it the focal length is not making the p.eq negative)

Correct me if im wrong, but yeah

 

[yugi]

hmm well according to the jones and couchman textbook for a parabola x^2=-4y it says that a=-1 and x=-2t and y=-t^2 so yeah

 

[alchetor]

hmm well according to the jones and couchman textbook for a parabola x^2=-4y it says that a=-1 and x=-2t and y=-t^2 so yeah

ooh okay, so focal lengths can be <0?
heh okay xD id better go revise :L

 

[xV1P3R]

If you have a to be eternally positive, it isn't consistent with the general point on the parabola (2ap,ap²) screwing you over when you have an upside down parabola.