Question

Find two different sets of parametric equations for the rectangular equation y = 6x − 5

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asked 2021-05-21

Find two different sets of parametric equations for the rectangular equation \(y = 6x − 5\)

Answers (1)

2021-05-22

Step 1
Given:
The rectangular equation is:
\(y=6x−5\)
We have to find the two different sets of parametric equations for a given rectangular equation.
Step 2
Now Consider,
t is a parameter for the given rectangular equation.
\(x=t\Rightarrow y=6t-5\)
Then the set is:
\({(x,y)|x=t\ and\ y = 6t-5}\)
Consider,
t is a parameter for the given rectangular equation.
\(x=t+2\)
\(\Rightarrow y=6(t+2)-5\)
\(\Rightarrow y=6t+12-5\)
\(\Rightarrow y=6t+7\)
Then the set is:
\({(x,y)|x=t+2\ and\ y = 6t+7}\)
Hence, the two different sets of parametric equations for a given rectangular equation are:
\({(t,6t-5)x=t\ and\ y=6t-5}\ and\ {((t+2),(6t+5))|x=t+2\ and\ y = 6t+7}\)

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