In xy plane a point P moves in such a way that $\angle APB = 30^\circ$ , where points $A$ and $B$ are $ (0,0) (10,0)$ respectively , then area (A) bounded by the locus is :
(a) less than$ 200 \pi$ sq.units
(b) greater than $100\pi$ sq. units
(c) greater than $25\pi$ sq. units
(d) less than $100\pi$ sq. units
My Approach : I assumed P point as $(x,y)$ and using the condition of $\angle APB = 30^\circ$ and using the slope formula of straight lines I found the locus of P which is quadratic in $x$ and $ y$ . And the area of triangle $PAB$ came out as $10y/2$ but I am not able to conclude . I also tried to use geometry as $\angle APB = 30^\circ$ and the locus came out to be circle by which (d) option came but i am not sure about (c) part . please help