[" (ii) "x-2y,=3],[3x+y,=16],[," [M.P."2009]]

3x-2y=3,2x+y=16

x+2y+4=0,3x=-4y-16

2x-3y=14,5x+2y=16

7x - 2y = 3 , 22x - 3y = 16 .

For any scalar p prove that =|[x,x^2, 1+p x^3],[y, y^2, 1+p y^3],[z, z^2 ,1+p z^3]|=(1+p x y z)(x-y)(y-z)(z-x) .

A variable chord of the circle x^2+y^2=4 is drawn from the point P(3,5) meeting the circle at the point A and Bdot A point Q is taken on the chord such that 2P Q=P A+P B . The locus of Q is (a) x^2+y^2+3x+4y=0 (b) x^2+y^2=36 (c) x^2+y^2=16 (d) x^2+y^2-3x-5y=0

A variable chord of the circle x^2+y^2=4 is drawn from the point P(3,5) meeting the circle at the point A and Bdot A point Q is taken on the chord such that 2P Q=P A+P B . The locus of Q is (a) x^2+y^2+3x+4y=0 (b) x^2+y^2=36 (c) x^2+y^2=16 (d) x^2+y^2-3x-5y=0

Find the correct choice. {:("(A)"5x+2y=16),(" "7x-4y=2):}}" (P)no solution" {:("(B)"5x+2y=16),(" "3x+(6)/(5)y=2):}}" (Q) unique solution" {:("(C)"5x+2y=16),(" "(15)/(2)x+3y=24):}}" (R) infinite number of solution"

Evaluate : (viii) (3x + 4y) (3x -4y) (9x^2 + 16y^2)

{:(3x + y = 18),(6x + 2y = 16):}