Parabola.. (1 Viewer)

[- Alex -]

This question might sound stupid but y=x^2+bx+c and x^2=4ay both represents a parabola...what is the difference? :S

 

[untouchablecuz]

 

[blaze.bluetane]

y=ax^2 +bx +c (GENERAL FORM)
x intercepts at
x=(-b+-sqrt(b^2-4ac))/2
y intercept at y=c


x=4ay (PARAMETRIC FORM)
The definition of a parabola in terms of one variable p (parameter): (2ap,ap^2)
passes through origin (the only intercept)
directrix: x=-a
focus=(0,a)

 

[jet]

y=ax^2 +bx +c (GENERAL FORM)
x intercepts at
x=(-b+-sqrt(b^2-4ac))/2
y intercept at y=c


x=4ay (PARAMETRIC FORM)
The definition of a parabola in terms of one variable p (parameter): (2ap,ap^2)
passes through origin (the only intercept)
directrix: x=-a
focus=(0,a)

By definition the first parabola also has a focus/directrix as every parabola is a locus, and remember that parametrics are not a 2u topic. It would seem more correct to define the second equation as a 'special' form of the first, which passes through the origin, (0,0)

 

[untouchablecuz]

 

[cutemouse]

x^2=4ay has vertex at (0,0) and focus at (0,a)

 

[tommykins]

y=ax^2 +bx +c (GENERAL FORM)
x intercepts at
x=(-b+-sqrt(b^2-4ac))/2
y intercept at y=c


x=4ay (PARAMETRIC FORM)
The definition of a parabola in terms of one variable p (parameter): (2ap,ap^2)
passes through origin (the only intercept)
directrix: x=-a
focus=(0,a)

TECHNICALLY x^2 = 4ay isn't the parametric form.

 

[addikaye03]

By definition the first parabola also has a focus/directrix as every parabola is a locus, and remember that parametrics are not a 2u topic. It would seem more correct to define the second equation as a 'special' form of the first, which passes through the origin, (0,0)

(x-h)^2=+-4a(y-k) [General form] Where V(h,k) S(h, k+-a) is still 2u material though. But yeah i agree about it should be considered as a "special case".

 

[- Alex -]

Thanks guys i know it now..i've been told they are the same but with x^2+bx+c=0 dealing with algebraic properties such as the roots and x^2=4ay dealing with geometric properties such as the directrix and focus