Question

if sum of slope of line represented by x²+kxy-3y²=0 is twice there product then value of k is___​

Answer 1

The value of k is - 2

Given equation is

             $x^{2}+kxy-3y^{2}=0$

Comparing with,

             $ax^{2}+2hxy+by^{2}=0$

Here,

               a = 1, 2h = k, b = -3

We know that,

     Sum of slopes = -2h/b

                              = -k/-3

                              = k/3

     Products of slopes = a/b

                                     = -1/3

Given,

   Sum of slopes = 2(product of slopes)

                      k/3 = -2/3

                      k  =  - 2

∴ The value of k is - 2