Question

A. Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.
b. Eliminate the parameter to find a Cartesian equation of the curve.

x=1 + 3t, y= 2-t^2

Answer 1

Answer:

y  =  2 -  ( x - 1)²/9

Step-by-step explanation: See Annex

As the parameter t increases,  the value of x increases and the value of y decreases, we get the figure of the annex ( the arrow in the Annex indicates the way of the curve with t increasing.

b) to eliminate the parameter:

x  =  1  + 3*t    (1)          y  =  2  -  t²  (2)

Then  from equation (1)  t  = ( x  - 1 ) / 3

plugging that value in equation (2)

y  =  2  -  [ (  x  -  1 ) / 3 ]²

y  =  2  - ( x² + 1 - 2*x)/9

9*y  =  18  - x² + 1 - 2*x    or    y  =  2 -  ( x - 1)²/9

The curve is a parabol

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