Question

Eliminate the parameter of the following equations and write in rectangular form in terms of x and y.

x=2+3cost, y=1−sint

Show all work for full credit.

Answer 1

Solve for cos(t) and sin(t):

x = 2 + 3 cos(t) ⇒ cos(t) = (x - 2)/3

y = 1 - sin(t) ⇒ sin(t) = 1 - y

Recall the Pythagorean identity,

sin²(t) + cos²(t) = 1

It follows that

((x - 2)/3)² + (1 - y)² = 1

or

(x - 2)²/9 + (y - 1)² = 1