" (i) "(9y^(2)-4x^(2))(81y^(4)+36x^(2)y^(2)+16x^(4))

If x=3 and y=-1, find the values of each of the using identity: (9y^(2)-4x^(2))(81y^(4)+36x^(2)y^(2)+16x^(4))

If x=-2 and y=1, by using an identity find the value: (4y^(2)-9x^(2))(16y^(4)+36x^(2)y^(2)+81x^(4))

If x=3\ a n d\ y=-1, find the values of each of the using identity: (9y^2-4x^2)(81 y^4+36 x^2y^2+16 x^4)

A variable chord of the circle x^(2)+y^(2)=4 is drawn from the point P(3,5) meting the circle at the point A and B. A point Q is taken on the chord such that 2PQ=PA+PB The locus of Q is x^(2)+y^(2)+3x+4y=0x^(2)+y^(2)=36x^(2)+y^(2)=16x^(2)+y^(2)-3x-5y=0

If x=1 and y=-2; by using the identity find the following : (i) (4y^2-9x^2)(16y^4+36x^2y^2+81x^4) (ii) (x+2y)(x^2-2xy+4y^2)

If x=-2\ a n d\ y=1, by using an identity find the value: (4y^2-9x^2)(16 y^4+36 x^2y^2+81 x^4)

Find the eccentricity, length of latus rectum, centre, foci, vertices and the equatioin to the dircctriccs of the hyperola. (i) 4x^(2)-5y^(2)-16x+10y+31=0 (ii) 5x^(2)-4y^(2)+20x+8y-4=0 (iii) 4(y+3)^(2)-9(x-2)^(2)=1 (iv) 4x^(2)-9y^(2)-8x-32=0

For all real values of m, the straight line y=mx+sqrt(9m^(2)-4) is a tangent to which of the following certain hyperbolas? (a) 9x^(2)+4y^(2)=36 (b) 4x^(2)+9y^(2)=36 (c) 9x^(2)-4y^(2)=36 (d) 4x^(2)-9y^(2)=36

Factorize following experssions (i) x^(4)-y^(4)" (ii)"9a^(2)-(2x-y)^(2)" (iii)"4x^(2)-9y^(2)-6x-9y

Factorize following experssions (i) x^(4)-y^(4)" (ii)"9a^(2)-(2x-y)^(2)" (iii)"4x^(2)-9y^(2)-6x-9y