Question

Find a set of parametric equations for the rectangular equationt=2-xy=1-5x^2

Answer 1

Parametric Equations

We are given the following equations:

`\begin{gathered} t=2-x \\ y=1-5x^2 \end{gathered}`

We are required to find a set of parametric equations.

Let's set 't' as the parameter. We need to find x and y as functions of t.

Solving the first equation for x:

`x=-t+2`

Substituting in the second equation:

`\begin{gathered} y=1-5(-t+2)^2 \\ \text{Expanding the square:} \\ y=1-5(t^2-4t+4) \\ \text{Operating:} \\ y=1-5t^2+20t-20 \\ \text{Simplifying:} \\ y=-5t^2+20t-19 \end{gathered}`

This corresponds to the second choice