Please help me with this precal problem

Question

A pair of parametric equations is given. x = 4 cos (t), y = 5 sin (t),0<(less than or equal to)t<(less than or equal to)2pi

Find a rectangular-coordinate equation for the curve by eliminating the parameter.

Answer 1

We can use the Pythagorean identity cos^2x+sin^2x = 1 to show that

x^2 + (4y/5)^2 = 16, or

x^2 + y^2

----- ----- = 1,

16 25

which is the equation of an ellipse.

Answer 2

Hello Kayley,

You could do this using the equation cosine squared + sine squared = 1.

Solve the first equation for cos t and the second equation for sin t. Then square both sides of each equation and add them together and see if you can write the final answer.

Tom S.