SOLUTION: x=2sec(t) and y=4tan(t). Place the parametric equations in rectangular form. Identify the conic. Show all algebraic support. Please help me out!

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: x=2sec(t) and y=4tan(t). Place the parametric equations in rectangular form. Identify the conic. Show all algebraic support. Please help me out!      Log On


   

Question 185921: x=2sec(t) and y=4tan(t). Place the parametric equations in rectangular form. Identify the conic. Show all algebraic support. Please help me out!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
and ... Start with the given parametric equations.


and ... Square both sides for each equation.



and ... Square the right sides and simplify



and ... Isolate for and .


and Rearrange the equations



Now remember, is an identity


... Start with the given identity


... Plug in and


... Subtract from both sides.


Rearrange the equation.


Now the equation is in rectangular form


Note: the last equation is in the form of a hyperbola.