Final answer:
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