Question

Find parametric equations for the path of a particle on the circle ( x² + (y − 3)² = 16 ).

a) ( x = 4cos(t),; y = 3 + 4sin(t) )
b) ( x = -8cos(t),; y = 3 - 8sin(t) )
c) ( x = 4cos(t),; y = 3 - 4sin(t) )
d) ( x = -4cos(t),; y = 3 + 4sin(t) )

Answer 1

The correct parametric equations for the particle's path on the given circle are (x = 4cos(t), y = 3 + 4sin(t)), which match option a.

Step-by-step explanation:

To find the parametric equations for the path of a particle on the circle given by x² + (y − 3)² = 16, you can use the following standard parametric equations for a circle centered at (h, k) with radius r:

• x(t) = h + r*cos(t)
• y(t) = k + r*sin(t)

From the given equation, we can see that the center of the circle is at (0, 3) and the radius is 4. Therefore, the correct parametric equations would be:

x(t) = 0 + 4*cos(t) = 4cos(t)

• y(t) = 3 + 4*sin(t) = 3 + 4sin(t)

So the answer is option a) (x = 4cos(t), y = 3 + 4sin(t)).