Chapter 10: Q. 8. (page 694)

In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.
$x = t - 3, y = 2 t + 4 0 \leq t \leq 2 .$

Short Answer

Expert verified

The answer is $y - 2 x - 10 = 0 .$

Step by step solution

Step 1. Given information.

$x = t - 3 y = 2 t + 4$

is given.

Step 2. Calculation.

Graph the curve defined by the parametric equations -

$x = t - 3 y = 2 t + 4 0 \leq t \leq 2$

$t$	$x$	$y$	data-custom-editor="chemistry" $(x, y)$
$0$	$2$	1	(2,1)
1	5	2	(5,2)
2	8	3	(8,3)

We find the rectangular equation by eliminating the parameter t from the parametric equations.

$x = t - 3 t = x + 3$

Put the value of t-

$y = 2 t + 4 y = 2 (x + 3) + 4 y = 2 x + 6 + 4 y = 2 x + 10 y - 2 x - 10 = 0 .$

Thus, the equation is $y - 2 x - 10 = 0 .$

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In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.
$x = t - 3, y = 2 t + 4 0 \leq t \leq 2 .$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

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In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.x=t-3,y=2t+40≤t≤2.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.
$x = t - 3, y = 2 t + 4 0 \leq t \leq 2 .$