The rectangular form of the parametric equations x = 4cos(t) – 3 and y = 5sin(t) + 2 is shown in the option third, option third is correct.
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.
The missing options are in the attached picture please refer to the picture.
We have two parametric equations:
x = 4cos(t) – 3 and
y = 5sin(t) + 2
From the options plug x and y values in the equation:
[tex]\rm \dfrac{(x+3)^2}{16}+\dfrac{(y-2)^2}{25}=1\\[/tex]
[tex]\rm \dfrac{(4cos(t)-3+3)^2}{16}+\dfrac{(5sin(t)+2-2)^2}{25}=1\\[/tex]
[tex]\rm \dfrac{(4cos(t))^2}{16}+\dfrac{(5sin(t))^2}{25}=1\\[/tex]
cos²t + sin²t = 1 (true)
Thus, the rectangular form of the parametric equations x = 4cos(t) – 3 and y = 5sin(t) + 2 is shown in the option third, option third is correct.
Learn more about the parametric function here:
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