Why parametric equations of the parabola #y^2 = 4ax# is #y =2at# and #x = at^2# . why can't #y =4at# and #x = 4at^2#. Because #y = 4at# and #x = 4at^2# also satisfies the equation #y^2 = 4ax# right ?
1 Answer
Jan 11, 2018
Parametric equations are not unique.
Explanation:
Start with
y is the domain and it is
x is the range and it is
Let's check your parametric equations
y has the domain
x has the range
Let
The two graphs are identical.
I am sure that you can find other parametric equations for the same graph. For example,