How Do I Find P1 and P2 for a Parametrized Curve?

[Niall101]

Question: Attached.

Attempt.

I know I have to find P1 and p2 depending on x and L to satisfy

ax^2 + bxy + cy^2 + dx + ex + f =0

I have tried looking at the ladder when resting on axis to get a better picture but cannot see where to go next.

 

[LCKurtz]

You don't want to start with the general equation of a conic because you don't know ahead of time it even is a conic. I know, the question tells you that, but you shouldn't assume it.

Here's a picture of the slanted ladder:

Figure out a and b in terms of x, L, and λ. You will need to use the trig functions of θ which you can also get in terms of x, L, and λ. That should get you started.

 

[Niall101]

Thanks so much! I am going to work more on this today after class.