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

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

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

Respuesta :

Otras preguntas

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