Question

Find the nature of the conic 2x^2+xy-y^2-6-0

Answer 1

comparing this with general equation Ax^2 + Bxy + Cy^2 +Dx + Ey + F = 0
we get

A = 2, B = 1, C = -1

now B^2 -4*A*C  = (1*1) - 4* 2 *(-1)
                           =1+8 = 9 >0 

=> equation represents hyperbola.