Question

Eliminate the parameter, t, in the parametric equations, x = 3cos(t) and y = -6sin(t).

A) 2 x2 + y2 = 36
B) x2 + y2 = 2
C) 4 x2 + y2 = 36
D) x2 + y2 = 36

Answer 1

Recall that

cos²(t) + sin²(t) = 1

Then solving for cos(t) and sin(t), we have

x = 3 cos(t)   ===>   cos(t) = x/3

y = -6 sin(t)   ===>   sin(t) = -y/6

so that the above identity gives us

(x/3)² + (-y/6)² = 1

x²/9 + y²/36 = 1

36 (x²/9 + y²/36) = 36

(C) 4x² + y² = 36

Answer 2

The parametric equation in the Cartesian form is 4x² + y² = 36 the correct choice is (C).

What are parametric equations?

A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.

We have two parametric equations:

x = 3cos(t) and

y = -6sin(t).

As we know, the trigonometric identity:

sin²θ + cos²θ = 1

For checking the option (A):
2x² + y² = 36

= 2(3cos(t))² + (-6sin(t))²

= 18cos²t + 36sin²t ≠ 36

Similarly, for checking the option:

4x² + y² = 36

= 4(3cost)² + (-6sint)²

= 36cos²t + 36sin²t

= 36(cos²t + sin²t)

= 36(1) = 36

Thus, the parametric equation in the Cartesian form is 4x² + y² = 36 the correct choice is (C).

Learn more about the parametric function here:

brainly.com/question/10271163

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