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

question 191

Multiple Choice

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)

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