Question

what is the polar form of the parametric equations x=4t and y=t^2

Answer 1

Answer:

Given that,

The parametric equations x=4t and y=t^2

To find the polar form of the parametric equations

Explanation:

we know that,

The polar form of the equation is expressed in terms of r and theta,

The conversion of Cartesian co-ordinate to Polar co-ordinate is given by,

$\begin{gathered} r^2=x^2+y^2 \\ \\ \tan\theta=\frac{y}{x} \end{gathered}$

Using this we get,

$r^2=(4t)^2+(t^2)^2$

$r^2=16t^2+t^4$$r=\sqrt{16t^2+t^4}$

we have that,

$\tan\theta=\frac{t}{4}$$t=4\tan\theta$

Substitute this we get,

$r=\sqrt{16t^2+t^4}$$undefined$