The sum of squares of all possible values of k, for which area of the region bounded by the parabolas 2y^2= kx and ky^2=2 (y-x ) is maximum, is equal to :

Question

Accepted Answer

Correct answer: 8. (8) ky^2=2 (y-x )2y^2= kx Point of intersection ky^2= ( y-2y^2k ) y=0 ky=2 ( 1-2yk ) ky+ 4yk=2y= 2k+ 4k= 2kk^2+4A= 0.05em 0.05em((y- ky^22)- ( 2y^2k )) dy= y^22-(( k2+ 2k) y^33)_0^ 2kk^2+4= ( 2kk^2+4 )^2( 12- k^2+42k 13 2kk^2+4)(= 16 4 ( 1k+ 4k )^2)A M G M (k+ 4k)2 2k+ 4k 4 Area is maximum when k= 4k k=2 ,-2

$The sum of squares of all possible values of k, for which area of the region bounded by the parabolas 2 y^{2} = kx and ky^{2} = 2 (y - x) is maximum, is equal to :$

Solution

More Area Under Curves PYQs