Answer:
and
Step-by-step explanation:
We have the following system of equations:
and
To solve the problem, we need to equal the two equations:
⇒
⇒
⇒
So you need to find two numbers that added equal to 5 and multiplied equal to 4. These two numbers are and
.
Then, the factorized form of the polynomial is: .
The, the solution to the system of equations is: and
.
The rectangular equation for given parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π is which is an ellipse.
For given question,
We have been given a pair of parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π.
We need to convert given parametric equations to a rectangular equation and sketch the curve.
Given parametric equations can be written as,
x/2 = sin(t) and y/(-3) = cos(t) on 0 ≤ t ≤ π.
We know that the trigonometric identity,
sin²t + cos²t = 1
⇒ (x/2)² + (- y/3)² = 1
⇒
This represents an ellipse with center (0, 0), major axis 18 units and minor axis 8 units.
The rectangular equation is
The graph of the rectangular equation is as shown below.
Therefore, the rectangular equation for given parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π is which is an ellipse.
Learn more about the parametric equations here:
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