Question

Write the corresponding rectangular equation for the curve represented by the parametric equation x=9t-2, y=4t+3 by eliminating the parameter.

a. 4x-y+35=0
b. 4x-9y+35=0
c. 4x-9y+11=0
d. 4x+y-35=0
e. 4x+9y-11=0

Answer 1

b. 4x-9y+35=0

Explanation:

You want the general form equation for the line represented by the parametric equations ...

• x = 9t -2
• y = 4t +3

Eliminate the parameter

We can eliminate the parameter the same way we would eliminate a variable when solving a pair of equations. Here, we can subtract 9 times the second equation from 4 times the first:

4(x) -9(y) = 4(9t -2) -9(4t +3)

4x -9y = 36t -8 -36t -27 . . . . . . . eliminate parentheses

4x -9y +35 = 0 . . . . . . . . . . add 35

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Additional comment

Another way to do this is to solve one equation for t, then substitute for t in the other equation. That involves fractions and can be somewhat messier.

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