Just A Minute....

But if we remove the modulas --- (√x²+30² ) + (√x²+50²) = 20 which means that the sum of distances of (x,0) from the points (0,30) and (0,50) is constant,i.e,the locus of x is a ellipse. So x should have infinite values.

soumya u r right ...x has infinite values ...bot not INTEGRAL infinite values....
btw yagyadutt ji ...thank you for taking efforts....lekin yahape apko itni mehnat karneki zarurat nahi u can use latex .....just go to this link ...
http://targetiit.com/latex/editor.php?target=message&html

I dont see any prob in karna's soln....

Thanks everyone

Karna's & Yagyadutt's

both the solutions r accepted