Parametric Equations and And a Parameter Interval for the Motion $x=4 t^{2}, y=2 t, x \leq t \leq \infty$

Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph
traced by the particle and the direction of motion.
- $x=4 t^{2}, y=2 t, x \leq t \leq \infty$

A) $x = y ^ { 2 }$ ; Entire parabola, top to bottom (from1st quadrant to origin to 2nd quadrant)


B) $y = x ^ { 2 }$ ; Entire parabola, right to left (from 1st quadrant to origin to 4 th quadrant)

C) $x = y ^ { 2 }$ ; Entire parabola, bottom to top (from 2nd quadrant to origin to 1st quadrant)


D) $y = x ^ { 2 }$ ; Entire parabola, left to right (from 4th quadrant to origin to 1st quadrant)