Eliminate the parameter t Then use the rectangular equation

Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t

x= sqrt 3t, y=3t-1, <t<

y=

Choose the plane curve represented by the given parametric equations.

Solution

x=sqrt3 t

squaring both sides

x²=3t

and y=3t-1

substituting x² for 3t

Therefore y=x²-1The given equation represents parabola .