The Parabola (1 Viewer)

[Noobtron]

Answer this Q, its fooled my teacher and the writers of the question and my friend, can someone answer this

Find the equation of the parabola that passes through 0,0 2,20 -2,4 with the axis parralel to the y axis. State the coordinates of the focus and the equation of the directrix

 

[Hikari Clover]

回复: The Parabola

it isnt that hard actually.....maybe,probably,not sure........

with the axis parralel to the y axis
means the parabola could be either concave up or down, or could be both....
in my opinion, i prefer concave up only.....
i found that a parabola with n-shape couldnot pass through that 3points at a time

so (x-h)^2=4a(y-k)
u sub 0,0 2,20 -2,4 into it respectively,and then find h,k,a,which would provide u focus and directrix.....

any1 else?

 

[wrxsti]

coords of focus is (0 , 1/20)
directrix y = -1/20

Simple question..... TOO SIMPLE.... im missing something arent I?

 

[NovaAesa]

Parabolas with axis parallel to the y-axis are in the form y=ax^2 + bx + c
so just sub in the points and do simultanious equations with 3 equations.

This leaves y = 3x^2 + 4x

Then rearange using completion of the square to get the other form of the parabola.

This gives: (x+ 2/3)^2 = 4 * 1/12(y+4/3)

So the vertex is (-2/3, -4/3) and the focal length is 1/12
This puts the focus at (-2/3, -5/4) and the directrix at y = -17/12

I hope thats all right....

 

[kooltrainer]

erm..

 

[ssglain]

So the vertex is (-2/3, -4/3) and the focal length is 1/12
This puts the focus at (-2/3, -5/4) and the directrix at y = -17/12
I hope thats all right....

I got that, but using (x - h)² = 4a(y - k)² as the equation of the parabola.

 

[Mattamz]

i think the question is a dud.

Similar case to this thread: http://community.boredofstudies.org/13/mathematics-extension-1/149645/parabolic-question.html

the axis of symmetry (and thus the directrix) are not parallel to the x or y axis. so you cant assume the equation of the parabola to be in the form:
y=ax^2 + bx +c
OR
(x-h)^2 = 4a(y-k)

 

[ssglain]

i think the question is a dud.

Similar case to this thread: http://community.boredofstudies.org/13/mathematics-extension-1/149645/parabolic-question.html

the axis of symmetry (and thus the directrix) are not parallel to the x or y axis. so you cant assume the equation of the parabola to be in the form:
y=ax^2 + bx +c
OR
(x-h)^2 = 4a(y-k)

Question says "... the axis parralel to the y axis", assuming, of course, "the axis" refers to the axis of symmetry.

 

[independantz]

the axis of symmetry (and thus the directrix) are not parallel to the x or y axis.

Eh isnt the directrix perpendicular to the axis of symmetry?