- #1

Jimmy5050

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**Parameterizing vector function for intersection of cylinder and plane**

## Homework Statement

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

## Homework Equations

## 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.

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