Eliminate the parameter in the equations x = t^2, y = t^4.

Question

And find its domain.?

Answer 1

The parametic equations are x = t² and y = t⁴

x = t²

Solve for t.

t = √x

Substitute t = √x in y = t⁴ .

y = (√x)⁴

y = [x^(1/2)]⁴

y = x²

The equation is a parabola (opens up) and it's vertex at origin.

Domain a parabola is all real numbers.

Domain of the function y = x² is all real numbers.