<PRE><B>Question 1143991</B>
&lt;br&gt;
Let&#39;s start with a generic set of parametric equations and see how it relates to the equation of an ellipse in rectangular coordinates.&lt;br&gt;
{{{x = a+b*cos(t)}}}
{{{y = c+d*sin(t)}}}&lt;br&gt;
The parameter is t; eliminate it using sin^2+cos^2=1.&lt;br&gt;
{{{cos(t) = (x-a)/b}}}
{{{sint(t) = (y-c)/d}}}&lt;br&gt;
{{{sin(t)^2+cos(t)^2 = (x-a)^2/b^2+(y-c)^2/d^2 = 1}}}&lt;br&gt;
The center is (a,c); the semi-major and semi-minor axes are (in some order) b and d.&lt;br&gt;
Now use that analysis for the given ellipse.&lt;br&gt;
The center is (a,c) = (5,-3), so the constants in the parametric equations for x and y must be 5 and -3, respectively.  That eliminates answer choice D.&lt;br&gt;
The semi-major axis is 6, in the y direction, so d is 6.  That makes answer choice C the only possible correct answer.&lt;br&gt;
It can be seen that answer choice C is in fact correct, because it shows the semi-minor axis having length b=2.&lt;br&gt;
ANSWER: C. x=5+2cos t, y=-3+6 sin t</PRE>