I have solved for part (a) and part (b), including showing OA, problem lies in showing OM... would appreciate some help for showing OM=$\displaystyle 2cos\theta+5sin\theta$
Thanks!!!
For OA, its far more simple! Draw a line perpendicular to the x-axis from the point (5,2). Let point on perpendicular line on x-axis be X.
So
$\displaystyle OX=5$.
$\displaystyle tan\theta= \frac{2}{XA}$
$\displaystyle cot\theta=\frac{XA}{2}$
$\displaystyle XA=2cot\theta$
$\displaystyle OA = 5+2cot\theta$