1)find the sides of rectangle with greatest possible perimeter inscribed in a semicircle . . . . 2)for what point P of the parobola ysq.=2px has the segment of inner normal at P the smallest length???

Dear sneha,

I recommend that you make a mirror image of the semicircle and the rectangle, flipping about the diameter. Than you will have a rectangle of double area inscribed into a full circle, and the question becomes : what rectangle inscribed into a circle has max area. The answer is the square, due to symmetry (I just restored that symmetry for you). So your initial rectangle inscribed into semicircle was [ r√2 ] x [ r/√2 ].

We are all IITians and here to help you in your IIT JEE preparation.

All the best.

 If you like this answer please approve it....

win exciting gifts by answering the questions on Discussion Forum

Sagar Singh

B.Tech IIT Delhi