If the equation `2^x+4^y=2^y + 4^x` is solved for `y` in terms of `x` where `x<0,` then the sum of the solution is (a) `x(log)_2(1-2^x)` (b) `x+(log)_2(1-2^x)` (c)`(log)_2(1-2^x)` (d) `x(log)_2(2^x+1)`

y=2^(1/((log)_x4) , then find x in terms of y.

Solve the equation tan^4x+tan^4y+2cot^2xcot^2y=3+sin^2(x+y) for the values of xa n dydot

Given the equation 4x^2+2sqrt(3)x y+2y^2=1 . Through what angle should the axes be rotated so that the term x y is removed from the transformed equation.

Shift the origin to a suitable point so that the equation y^2+4y+8x-2=0 will not contain a term in y and the constant term.

Statement 1 : The equations of the straight lines joining the origin to the points of intersection of x^2+y^2-4x-2y=4 and x^2+y^2-2x-4y-4=0 is x-y=0 . Statement 2 : y+x=0 is the common chord of x^2+y^2-4x-2y=4 and x^2+y^2-2x-4y-4=0

Suppose a x+b y+c=0 , where a ,ba n dc are in A P be normal to a family of circles. The equation of the circle of the family intersecting the circle x^2+y^2-4x-4y-1=0 orthogonally is (a) x^2+y^2-2x+4y-3=0 (b) x^2+y^2-2x+4y+3=0 (c) x^2+y^2+2x+4y+3=0 (d) x^2+y^2+2x-4y+3=0

Identify the type of conic section for each of the equations 1. 2x^(2) -y^(2) = 7 2. 3x^(2) +3 y^(2) -4x + 3y + 10 =0 3. 3x^(2) + 2y^(2) = 14 4. x^(2) + y^(2) + x-y=0 5. 11x^(2) -25y^(2) -44x + 50y - 256 =0 6. y^(2) + 4x + 3y + 4=0

The straight lines represented by the equation 135 x^2-136 x y+33 y^2=0 are equally inclined to the line (a) x-2y=7 (b) x+2y=7 (c) x-2y=4 (d) 3x+2y=4

Solve the system of equations in x,y and z satisfying the following equations x+[y]+{z}=3.1, y+[z]+{x}=4.3 and z+[x]+{y}=5.4

Draw the graph of the line given by the equation y=4x-1 " " (or) Use graphical method to solve the following system of equations 3x+2y=6, 6x+4y=8