Use a graph to estimate the coordinates of the highest point and the leftmost point on the curve
\[
x=5 t e^{t}, \quad y=6 t e^{-t} .
\]

Then find the exact coordinates.
Highest point:
Leftmost point: $\square$.
The curve has one horizontal asymptote and one vertical asymptote. Find them.
Horizontal asymptote: $y=\square$.
Vertical asymptote: $x=\square$.

Step 1 ：Estimate the coordinates of the highest point and the leftmost point on the curve by plotting the graph of the given parametric equations.

Step 2 ：Choose different values of t and calculate the corresponding x and y values.

Step 3 ：For t = -2: x = -10e^(-2), y = -12e^(-2)

Step 4 ：For t = -1: x = -5e^(-1), y = -6e^(-1)

Step 5 ：For t = 0: x = 0, y = 0

Step 6 ：For t = 1: x = 5e, y = 6e^(-1)

Step 7 ：For t = 2: x = 10e^2, y = 12e^(-2)

Step 8 ：Plot the points on a graph.

Step 9 ：Estimate the coordinates of the highest point to be approximately (5e, 6e^(-1)) and the leftmost point to be approximately (-10e^(-2), -12e^(-2)).

Step 10 ：Find the derivative of y with respect to x: dy/dx = 6e^(-3t)/5

Step 11 ：Set dy/dx = 0 and solve for t: 6e^(-3t)/5 = 0

Step 12 ：Since the exponential function e^(-3t) is always positive, there are no critical points.

Step 13 ：Therefore, the estimated coordinates of the highest point and the leftmost point are the exact coordinates.

Step 14 ：Highest point: (5e, 6e^(-1))

Step 15 ：Leftmost point: (-10e^(-2), -12e^(-2))

Step 16 ：Find the horizontal asymptote by taking the limit of y as x approaches positive or negative infinity: lim(x->∞) y = 0, lim(x->-∞) y = 0

Step 17 ：Therefore, the horizontal asymptote is y = 0.

Step 18 ：Find the vertical asymptote by taking the limit of x as t approaches positive or negative infinity: lim(t->∞) x = ∞, lim(t->-∞) x = -∞

Step 19 ：Therefore, the vertical asymptote is x = ±∞.