# Consider the parametric equations below. x = t^{2}, y = t^{7}.

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.

**Solution:**

Given x = t^{2}, y = t^{7}

Let us take a few sample values of t as input and get x, y values as output values.

t | -2 | -1 | 0 | 1 | 2 |
---|---|---|---|---|---|

x | 4 | 1 | 0 | 1 | 4 |

y | -128 | -1 | 0 | 1 | 128 |

We have got the following graph.

The horizontal axis is the x-axis and the vertical axis is the y-axis

The green curve is x and the violet curve is y

We can clearly see that if t increases, the green curve moves towards the positive x-axis and the violet curve moves towards the extreme ends of the y-axis

## Consider the parametric equations below. x = t^{2}, y = t^{7}

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.

**Summary:**

The graph for x = t^{2}, y = t^{7} has been plotted and the curves move towards the extremes of x, y axes as t increases.

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