Question

if one of the two lines 3x^2 +kxy-y^2=0 bisects an angle between the co-ordinate axes, then k=?​

Answer 1

Step-by-step explanation:

$\sf {3x}^{2} - kxy - {y}^{2} = 0 \\ \\ \\ \sf divided \: \: by \: \: {x}^{2} \\ \\ \\ \sf 3 - \frac{ky}{x} - \frac{ {y}^{2} }{ {x}^{2} } = 0 \\ \\ \\ \sf y = mx \\ \\ \\ \sf \frac{y}{x} = m \\ \\ \\ \sf {m}^{2} + km - 3 = 0 \\ \\ \\ \sf \: one \: \: of \: \: the \: \: line \: \: bisect \: \: co - drdinate \: \: axis \\ \\ \\ \sf put \: \: m = 1 \: \: or \: \: m = - 1 \\ \\ \\ \sf 1 + k - 3 = 0 \\ \\ \\ \sf k = 2 \\ \\ \\ \sf 1 - k - 3 = 0 \\ \\ \\ \sf k = - 2 \\ \\ \\ \sf \fbox{ \sf k = ±2 }$