Use the result, "the set of parametric equations for the circle is $x = h + r \cos \theta , y = k + r \sin \theta "$ to find a set of parametric equations for the circle with a center $( - 2,6 )$ and radius 5 .
A) $x = 5 + \cos \theta , y = 5 + \sin \theta$
B) $x = 4 + 25 \cos \theta , y = 36 + 25 \sin \theta$
C) $x = 2 - 5 \cos \theta , y = 6 + 5 \sin \theta$
D)$x = - \frac { 2 } { 5 } \cos \theta , y = \frac { 6 } { 5 } \sin \theta$
E) $x = - 2 + 5 \cos \theta , y = 6 + 5 \sin \theta$

Question

Quizplus · Accepted Answer

Using the formula, we get:
$$x = -2 + 5\cos \theta$$
$$y = 6 + 5\sin \theta$$
This puts the center at $(-2,6)$ and gives a radius of 5. Therefore, the correct choice is E.

Use the Result, "The Set of Parametric Equations for the Circle