Question

Consider the following. x = e^t, y = e^(−3t) . Eliminate the parameter to find a Cartesian equation of the curve.

Answer 1

To eliminate the parameter and find a Cartesian equation, solve for t in terms of x and substitute into the equation for y, resulting in y = x^(-3).

Step-by-step explanation:

To eliminate the parameter and find a Cartesian equation of the curve defined by x = e^t and y = e^(-3t), we need to solve for t in one equation and substitute into the other.

We can write t as t = ln(x) since x = e^t.

Then, substituting this into the equation for y gives us y = e^(-3*ln(x)).

Simplifying this, we use the property of exponents that e^(ln(a)) = a to get y = x^(-3), which is our Cartesian equation.