Question

Consider the following. Circle: x = h + r cos(theta), y = k + r sin(theta) Use the above to find a set of parametric equations for the conic. Circle: center: (−2, −3); radius: 6

Answer 1

Explanation:

The standard parametric equations for a circle with center (h, k) and radius r are:

x = h + r cos(theta)

y = k + r sin(theta)

Here, center is (−2, −3) and the radius is 6. Therefore, we have:

h = -2

k = -3

r = 6

Substituting these values into the standard equations, we get:

x = -2 + 6 cos(theta)

y = -3 + 6 sin(theta)

So the set of parametric equations for the circle is:

x(t) = -2 + 6 cos(t)

y(t) = -3 + 6 sin(t)

where t = theta.