(adsbygoogle = window.adsbygoogle || []).push({}); Parameterizing vector function for intersection of cylinder and plane

1. The problem statement, all variables and given/known data

Problem asks us to find the vector function of the curve which is created when the plane y= 5/2 intersects the ellptic cyl. (x^2)/4 + (z^2)/6 = 5

2. Relevant equations

3. The attempt at a solution

I know its going to be an ellipse formed....

I took the given ellptic cyl. equation, and divided by 5 to get (x^2)/20 + (z^2)/30 = 1.

***I parameterized by using x=cos(t) and z=sin(t) and got ((cost)^2)/20 + ((sint)^2)/30 =1.

Now, by looking at examples that are somewhat similar, I could tell the answer by looking at number relationships. However, I am unsure of the true way to go about getting my final solution.

My "made up way" of solving was to set either x or z to zero before parameterizing.

My final answers are x=(sqrt[20])cos(t) y=5/2 z=(sqrt[30])sin(t)

I checked my answer using a graphing program, and it is correct, but I am just unsure about going about the TRUE way of solving once I get to the part labeled *** above.

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Intersection of surface and plane.

**Physics Forums | Science Articles, Homework Help, Discussion**