Question

How to parametrize the equation y^2 = x^3?

Answer 1

y = x^(3/2)
x = y^(2/3)

let x = t^2

then y = (t^2)^ 3/2 = t^3
and x = (t^3)^ 2/3 = t^2

Answer 2

so first find y in terms of x then x in terms of y
and introduce an appropriate third parameter t
write x in terms of t and substitute in the formula relating y and x

(my last line wasn't really necessary as i had already defined x in terms of t but it served as a final check)

Answer 3

i would like to add there is a nice discussion here

http://www.physicsforums.com/showthread.php?t=14562

Answer 4

Hmm, so let's say, we have \(x^{10} = y^7\)
x = y^(7/10)
y = x^(10/7)

Let x = t^7, t= t^(10)

In this case, aren't we just switching the power of x and y for the parameter t?