Chapter 10, Problem 63RE

To determine

Tofind:the rectangular equation and graph the curve using parametric equation.

Answer to Problem 63RE

The rectangular equation is $\text{x+4y=2}$ and the graph here will be straight line.

Explanation of Solution

Given:

  $\text{x=4t-2, y=1-t}$ ; $\text{-}\infty \text{<t<}\infty$ .

Concept used:

The parametric equation has equation for each variable whereas rectangular equation has one equation

In rectangular equation it composed of variable like $\text{x and y}$ which can be graphed on a regular cartesian plane.

To convert parametric to rectangular $\text{t}$ should be eliminate so that function will be in the form of $\text{x and y}$ .consist of only one independent variable.

Calculation:

According to the given parametric equation:

  $\text{x=4t-2}$ …………… $\left(\text{i}\right)$

  $\text{y=1-t}$ …………….. $\left(\text{ii}\right)$

Multiply second equation by 4:

  $\text{4y=4-4t}$ ………………. $\left(\text{iii}\right)$

Adding equation $\left(\text{i}\right)$ and $\left(\text{iii}\right)$ :

  $\text{x+4y=2}$ .

Which is rectangular equation.

Since, the power or the degree of the equation is one so the graph will be straight line.

The graph of the equation $\text{x+4y=2}$ :

  

Here from the graph:

At $\text{x=0 y=0}\text{.5}$ .

At $\text{x=2 y=0}$ .

Hence, the rectangular equation is $\text{x+4y=2}$ and the graph here will be straight line.