Convert `x^2-y^2=4` into a polar equation.

Convert 2x^2+3y^2=6 into the polar equation.

Convert y=10 into a polar equation.

Convert (1+3i)/(1-2i) into the polar form.

Solve each the following pairs of equations by reducing them to a pair of linear equations. (vii) 10/x+y + 2/x-y = 4 15/x+y - 5/x-y = -2

The number of points P(x , y) lying inside or on the circle x^2+y^2=9 and satisfying the equation tan^4x+cot^4x+2=4sin^2y is______

Using matrix matrices, solve the following system of linear equations: x+2y-3z=-4,+2x+3y+2z=2,3x-3y-4z=11 .

Find the equation of tangents to the curve 4x^2-9y^2=1 which are parallel to 4y=5x+7.

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

If (a, 3) is point lying on graph of equation 5x+2y=-4 then a = ........