Parametric Equations: Sine & Cosine

Question

Eliminate the parameter, t, in the parametric equations, x = 6cost and y = 3sint.

Answer 1

x² = 36 cos² t, x² / 36 = cos² t

y² = 9 sin² t, y² / 9 = sin² t

(x² / 36) + (y² / 9) = sin² t + cos² t

(x² / 36) + (y² / 9) = 1

x² + 4y² = 36

Answer 2

x=6cost

y=3sint

x^2= 36cos^2(t)

y^2 = 9sin^2(t)

x^2/36 = cos^2(t)

y^2/9 = sin^2(t)

x^2/36 + y^2/9 = 1

x^2 + 4y^2 = 36

Answer 3

cos(t) = x/6

sin(t) = y/3

sin²(t) + cos²(t) = 1

(y/3)² + (x/6)² = 1

y²/9 + x²/36 = 1

x²/36 +4y²/36 = 1

x²+4y²= 36