Question

The Parametric Equations X=4sin²θ,Y=6cos²θ In The Given Cartedian Form. Y= With 0≤X≤4;

Answer 1

To convert the given parametric equations to Cartesian form, substitute the values of sin²θ and cos²θ into the equations. The resulting Cartesian form is Y = 6 - 6sin²θ.

Step-by-step explanation:

The given parametric equations are:

X = 4sin²θ

Y = 6cos²θ

To convert these parametric equations to Cartesian form, we can use the trigonometric identity: sin²θ + cos²θ = 1.

When we substitute the values of sin²θ and cos²θ into the equations, we get:
X = 4(1 - cos²θ)
Y = 6(1 - sin²θ)

Therefore, the Cartesian form of the given parametric equations is:
Y = 6 - 6sin²θ