Question

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

Answer 1

Given that,

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

To find the polar form of the parametric equations

Step-by-step 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=(y)/(x) \end{gathered}`

Using this we get,

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

`r^2=16t^2+t^4`
`r=√(16t^2+t^4)`

we have that,

`\tan\theta=(t)/(4)`
`t=4\tan\theta`

Substitute this we get,

`r=√(16t^2+t^4)`