Question

Consider the parametric equations below: x=t²-3, y=t+4, -3≤t≤3

a) Sketch the curve 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. _____ for 1 ≤ y ≤ 7

Answer 1

To sketch the curve, substitute values of t and plot the corresponding points. To find the Cartesian equation, eliminate the parameter t by rearranging the equations and substituting.

Step-by-step explanation:

To sketch the curve represented by the parametric equations x = t²-3 and y = t+4, we can substitute different values of t within the given range (-3≤t≤3) to find the corresponding points on the curve. By plotting these points on a graph, we can sketch the curve.

To find the Cartesian equation of the curve, we need to eliminate the parameter t. By rearranging the equations, we can express t in terms of x and substitute this value into the equation for y. This will help us find the equation of the curve in terms of x and y.

The Cartesian equation of the curve is y = x - 1, for 1 ≤ y ≤ 7.