Parabolas:(

[katkatkat]

if anyone could help me out with this i'd appreciate it im completly lost

Consider the ellipse (x^2/25) + (y^2/16) = 1. One foci is the focus of a parabola. One vertex is the vertex of this parabola.

a) How many different parabolas are possible?
b) determine the equation of the parabolas
c) Determine all co ordinates of the points of intersection of the parabolas algebraically.

 

[Unco]

For the ellipse: a = ?, b = ?, c = ?.

At one vertex of the ellipse, say \(\displaystyle \mbox{(a, 0)}\), a parabola sharing this vertex could have a focus at \(\displaystyle \mbox{(-c, 0)}\) or \(\displaystyle \mbox{(c, 0)}\). Draw a sketch to determine the respective distances from the vertex to the focus, that is, \(\displaystyle \mbox{p}\) for the parabola possibilities.

You'll have to be more specific as to where your difficulty is from there.

 

[katkatkat]

alright well ive gotten most of the question done just by playing around with different equations...what im stuck on now is the graphing.. if i have the equation y^2=32(x+5) how do i graph that?

 

[Unco]

You find the equation then sketch? Nice!

I'm sure you must have had it in the form

\(\displaystyle \mbox{y^2 = 4 \cdot 8 (x + 5)}\)

From:
Vertex at \(\displaystyle \mbox{(-5, 0)}\).
Focus at \(\displaystyle \mbox{(3, 0)}\).

The y-ordinate at \(\displaystyle \mbox{x=3}\) will be \(\displaystyle \mbox{2p=16}\). That should do for a rough sketch.