Question

Please help:

Eliminate the parameter
X=3tant Y=2sect

The final answer is a parabola but I'm not sure how to get there.

Answer 1

Solve for t in the X = ... equation and sub that in for t in Y = ...
I'll get you started. First solve for in X =..equation: \[x = 3 \tan(t) \implies t = \arctan \left( \frac{ x }{ 3 } \right)\] Let's plug this value of t in for t in y =... equation.\[\therefore y=2 \sec(\arctan (x/3))\] Do you understand?

@blueglass

Answer 2

I've been taught a method where you square everything and set sides equal to each other..are you familiar with that?

Answer 3

for example, eventually I get: