Parametric

Hi, how would I find the Cartesian form of this curve?
I rearranged f(t) for t but this results in square rooting and so part of the curve might be lost
The answer is 8y^2 = x^3 + 2x^2

t^2-1 looks a common factor? so y^2 = ...

Yurp ion understand any of that. 🤷

Haha parametric curves are written implicitly in terms of another variable (the parameter). In this case the parameter is t. To get the Cartesian form of the equation (in terms of x and y only) we need to eliminate the parameter t. In this case squaring y to get terms of t^6, t^4 and t^2 allow us to make a substitution which is in terms of x. To get this substitution you rearrange x = 2t^2 - 2 to make t^2 the subject

From their history, Im not sure the previous post was serious, but it would be slightly simpler here to use the t^2-1 factor directly so
y = t(x/2)
then square and sub for t^2.

Haha parametric curves are written implicitly in terms of another variable (the parameter). In this case the parameter is t. To get the Cartesian form of the equation (in terms of x and y only) we need to eliminate the parameter t. In this case squaring y to get terms of t^6, t^4 and t^2 allow us to make a substitution which is in terms of x. To get this substitution you rearrange x = 2t^2 - 2 to make t^2 the subject