Question

How do you convert `r = 4 csc (theta) cot (theta)` to rectangular form?

Answer 1

`y^2 =4x`

Explanation:

If the rectangular coordinate of a point be `(x,y)` and its corresponding polar coordinate be `(r,theta)` then we know that `x = rcostheta and y = rsintheta`

Our given equation in polar form is
`r = 4 csc (theta) cot (theta)=4/sintheta*costheta/sintheta`
`=>rsin^2theta =costheta`

Multiplying both sides by r
`=>r^2sin^2theta =4rcostheta`
`=>(rsintheta)^2 =4rcostheta`

Putting `rcostheta=x and rsintheta=y` we have the equation in rectangular form

`=>y^2 =4x`