Question

1) What is the shape of the graph of the following parametric equations?

x = 3 cos t and y = 2 sin t + 1
A. circle B. ellipse C.hyperbola D.parabola

Answer 1

The shape of the graph of the parametric equations given is:

• B. ellipse.

Explanation:

By inserting each of the equations given in a graphing calculator (Annex 1), it can be identified that both the first and second equations have an elliptical or ellipse shape, which is characterized by being periodic in the two directions in which it runs. Thus, the equation x = 3 cos t runs with elliptical motion on the Y-axis of the Cartesian plane, while the equation y = 2 without t + 1 runs with elliptical motion on the X-axis.