Question

the equation below gives parametric equations and parameter intervals for the motion of a particle in the xy - plane. identify the particles 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 = 5t + 3, y = 25t^{2}, -\inftyfind a cartesian equation for the particles path
$y=(x - 6)^{2}$

Explanation:

Step1: Solve \(x = 5t+3\) for \(t\)

From \(x = 5t + 3\), we get \(t=\frac{x - 3}{5}\).

Step2: Substitute \(t\) into \(y = 25t^{2}\)

Substitute \(t=\frac{x - 3}{5}\) into \(y = 25t^{2}\). Then \(y=25(\frac{x - 3}{5})^{2}\).

Step3: Simplify the equation

$$
LATEXBLOCK0
$$

Answer:

\(y=(x - 3)^{2}\)