Question

Please help me to find the separate equations of the line represented by following equations:
a) x^2+2(cosec a)xy-y^2=0
b) x^2+2xy. tan a-y^2=0

Answer 1

These two equations do not represent a (single) line. They are two different curves. For certain values of a, they overlap.

Answer 2

a) x^2-y^2 = 0
represents the lines y = ±x

Ax^2+Bxy+Cy^2=0 represents the same lines rotated through an angle θ such that

cot2θ = C-A/2B

so, we have cot2θ = 1/2 sin(a)

similarly for (b)