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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.

Consider the parametric equations below. x = t2, y = t7.
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 = t2, y = t7

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.

curves of the parametric equations x = t2, y = t7

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 = t2, y = t7
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 = t2, y = t7 has been plotted and the curves move towards the extremes of x, y axes as t increases.

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