P IS A VARIABLE POINT ON THE ELLIPSE   x²/a²+y²/b²-1=0, WITH AA’ AS THE MAJOR AXIS .THEN WHAT IS THE MAXIMUM VALUE OF THE AREA OF TRIANGLE APA’?

When p ia at A or A' area=0, as p starts moving towards the minor axis area increases and therefore area is maximum at (0,+b) or (0,-b) -

hence area=1/2[a(b-0)+0+(-a)(0-b)=ab