Rewrite the following parametric equations in rectangular form.

x=e^3t
y=e^-t

1 answer

To rewrite the parametric equations x = e^3t and y = e^-t in rectangular form, we can eliminate the parameter t by using the exponent rules for multiplication and division.

Starting with x = e^3t, we know that e^3t can be rewritten as (e^3)^t. Similarly, e^-t can be rewritten as 1/e^t.

Therefore, x = e^3t can be rewritten as x = (e^3)^t, and y = e^-t can be rewritten as y = 1/e^t.

This gives us the rectangular form equations:
x = (e^3)^t
y = 1/e^t