Graph the Cartesian equation: x=4t^2, y=2t

[Fatima Hasan]

Homework Statement

Parametric equations 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.

(1)$x = 4t^2$
(2) $y = 2t$ , $- \infty ≤ t ≤ \infty$

Homework Equations

-

The Attempt at a Solution

Square the second equation :
$y^2 = 4 t^2$ (3)
Subtract (3) - (1):
$y^2 - x = 0$
$y^2 = x$
This equation forms a parabola .
When $t = - 1$ , $x=4$ and $y=-2$
When $t = 1$ , $x = 4$ and $y=2$
From bottom to top.

Is my answer correct ?

 

[Mark44]

Homework Statement

Parametric equations 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.

(1)$x = 4t^2$
(2) $y = 2t$ , $- \infty ≤ t ≤ \infty$

Homework Equations

-

The Attempt at a Solution

Square the second equation :
$y^2 = 4 t^2$ (3)
Subtract (3) - (1):
$y^2 - x = 0$
$y^2 = x$
This equation forms a parabola .
When $t = - 1$ , $x=4$ and $y=-2$
When $t = 1$ , $x = 4$ and $y=2$
From bottom to top.
View attachment 231783
Is my answer correct ?

Looks good!

 

[fresh_42]

Yes, it is. I'm not quite sure what is meant by "Indicate the portion of the graph traced by the particle", but I assume it is the parabola itself.