Answer: r=16tan theta sec theta
Step-by-step explanation:
I have this question on my test but all the answers are different except that one
The polar form of the parametric equation is option (A), r = 16 tan theta sec theta is the correct answer.
Polar form of a complex number is represented by a line whose length is the amplitude and by the phase angle. A polar form of a vector is denoted by ( , ) , where represents the distance from the origin and represents the angle measured from the -axis.
Given the parametric equations x=4t and y=t².
Consider x= 4t
⇒ t = x/4
Now substitute t in y equation,
[tex]y= (\frac{x}{4} )^2[/tex]
[tex]y=\frac{x^2}{16}[/tex]
We know that in polar form,
x= r cosθ and y= r sinθ
Now y becomes
r sinθ= [tex]\frac{r^2\cos^2\theta}{16}[/tex]
16 r sin θ = r² cos²θ
r = 16 sinθ/cos²θ
⇒r =16 tanθ secθ
Hence we can conclude that the polar form of the parametric equation is option (A), r = 16 tan theta sec theta is the correct answer.
Learn more about the polar form here:
brainly.com/question/2272407
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