x Turn on thread page Beta
 You are Here: Home >< Maths

# FP2 - parabolas watch

1. Find an equation of the line which is a tangent to both the parabola with equation y^2 = 4ax and the parabola with equation x^2 = 4ay.
2. Well, those are inverse functions, aren't they? So they must be reflected in y=x...
3. (Original post by henryt)
Well, those are inverse functions, aren't they? So they must be reflected in y=x...
thanks for that.
4. Let's consider the general point (at^2, 2at) on the first parabola. The equation of the tangent at that point is:
y = (1/t)x + at

Now, let's see where this tangent intersects the other parabola:
x^2 = 4a((1/t)x + at) = (4a/t)x + 4a^2t
=> x^2 - (4a/t)x - 4a^2t = 0

We want them to intersect only once, so:
(4a/t)^2 - 4 * 1 * (-4a^2t) = 0
=> t^3 = -1
=> t = -1

So, the line is:
y = -(x + a)
5. (Original post by Popcorn)
thanks for that.
Well, sorry if I haven't actually done FP2 yet, and don't know what I'm talking about. Sheesh.
6. Just a side note: they're not really inverse functions (of each other).
7. (Original post by dvs)
Let's consider the general point (at^2, 2at) on the first parabola. The equation of the tangent at that point is:
y = (1/t)x + at

Now, let's see where this tangent intersects the other parabola:
x^2 = 4a((1/t)x + at) = (4a/t)x + 4a^2t
=> x^2 - (4a/t)x - 4a^2t = 0

We want them to intersect only once, so:
(4a/t)^2 - 4 * 1 * (-4a^2t) = 0
=> t^3 = -1
=> t = -1

So, the line is:
y = -(x + a)
Sorry a couple of years late but I don't understand what you did so that it intersects only once, can you explain this to me. thank you
8. anyone?

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 5, 2009
Today on TSR

Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams