Find parametric equations for the path of a particle that moves along the circle x2 + (y − 1)2 = 16 in the manner described. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.)

The parametric equations are determined by determining the trigonometric expressions associated to each component. Let 16 the square of the hypotenuse of a right-angled triangle, of which one of its extremes is set on the center of the circle C(0, 1). Then:

[tex]\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = 1[/tex]

By remembering the fundamental trigonometric identity ([tex]\cos^{2} t + \sin^{2}t = 1[/tex]) and comparing it with each term, the parametric equations are finally found:

[tex]x = 4\cdot \cos t[/tex]

[tex]y = 1 + 4\cdot \sin t[/tex]