Show that `(x^2+y^2)^4=(x^4-6x^2y^2+y^4)^2+(4x^3y-4x y^3)^2dot`

IF sin^(-1) X+ sin^(-1) y+ sin^(-1) z= pi , then prove that x^4 +y^4+ z^4 +4x^2 y^2 z^2 = 2(x^2 y^2 +y^2 z^2+z^2x^2).

The LCM and GCD of the two polynomilas is (x^2 + y^(2) ) (x^(4) + x^(2) y^(2) + y^(4)) and x^(2) -y^(2) one of the polynomial q(x) is (x^(4)-y^(4))(x^(2) +y^(2) - xy) find the other polynomials.

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi , then prove that x^(4)+y^(4)+z^(4)+4x^(2)y^(2)z^(2)=2(x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2))

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

The equation of the transvers axis of the hyperbola (x-3)^2+(y=1)^2+(4x+3y)^2 is x+3y=0 (b) 4x+3y=9 3x-4y=13 (d) 4x+3y=0

The equation of the circle which has normals (x-1).(y-2)=0 and a tangent 3x+4y=6 is (a) x^2+y^2-2x-4y+4=0 (b) x^2+y^2-2x-4y+5=0 (c) x^2+y^2=5 (d) (x-3)^2+(y-4)^2=5

Simplify (4x^2y)/(2 z^2) xx (6xz^3)/(20 y^4)

Find the slope at x=2 for y=x^(4)-4x^(3)

The equation of the transvers and conjugate axes of a hyperbola are, respectively, x+2y-3=0 and 2x-y+4=0 , and their respective lengths are sqrt(2) and 2sqrt(3)dot The equation of the hyperbola is 2/5(x+2y-3)^2-3/5(2x-y+4)^2=1 2/5(x-y-4)^2-3/5(x+2y-3)^2=1 2(2x-y+4)^2-3(x+2y-3)^2=1 2(x+2y-3)^2-3(2x-y+4)^2=1

By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=y^2(3y+k)