Answer:
[tex]r=4\csc \theta \cot\theta[/tex]
Step-by-step explanation:
The given parametric equations are;
[tex]x=t^2[/tex]
[tex]y=2t[/tex]
We make t the subject in the second equation to get:
[tex]t=\frac{y}{2}[/tex]
We substitute into the first equation to get:
[tex]x=(\frac{y}{2})^2[/tex]
We use the relation:
[tex]x=r\cos \theta[/tex] and [tex]y=r\sin \theta[/tex]
[tex]r\cos \theta=(\frac{r\sin \theta}{2})^2[/tex]
[tex]r\cos \theta=\frac{r^2\sin^2 \theta}{4}[/tex]
[tex]r=4\csc \theta \cot\theta[/tex]
An equation is formed of two equal expressions. The polar form of parametric equations x=t² and y=2t is r = 4cosecθ cotθ.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The following parametric equation x=t² and y=2t in the form of a polar equation can be written as,
y=2t
t = y/2
Substituting the value of y from the second equation in the first,
x = (y/2)²
Using the basic relation we can write, the value of x and y as,
x = r cosθ
y = r sinθ
substitute the value of x and y,
r cosθ = [(r sinθ)/2]
r sinθ = (r²sin²θ)/4
r = 4cosecθ cotθ
Hence, the polar form of parametric equations x=t² and y=2t is r = 4cosecθ cotθ.
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