For the parametric curve: x = 3 cos t, y = 3 sin t, eliminate the parameter and express in rectangular form. A) x² + y² = 3 B) 4x² + 4y² = 9 C) x² + y² = 1 D) x² - y² = 9 E) x² + y² = 9

Question

Quizplus · Accepted Answer

To eliminate the parameter t, we can use the trigonometric identity cos^2(t) + sin^2(t) = 1.

First, we can square both equations:
x^2 = 9cos^2(t)
y^2 = 9sin^2(t)

Then we can add them together:
x^2 + y^2 = 9(cos^2(t) + sin^2(t))
x^2 + y^2 = 9

This is the equation of a circle with center at the origin and radius 3. To express it in rectangular form, we simply need to rewrite it as x + y = 9 or x - y = 9.

Option E is the only one of the given choices that matches this equation, making it the best choice.

For the Parametric Curve: X = 3 Cos T, Y