Question

Find k, if one of the lines given by 6x² + kxy + y² = 0 is 2x + y = 0.

Answer 1

Given: 6x² + kxy + y² = 0 and 2x + y = 0.

To find: The value of k.

Solution:

• Now we have given that one of the lines given by 6x² + kxy + y² = 0 is 2x + y = 0.

• So, let the slope of the  2x + y = 0 be m1, then:

               m1 = -2                    ( from comparing y = mx + c )

• Now the given equation is: 6x² + kxy + y² = 0

• So in this, a = 6, h = k/2 and b = 1

               m1 + m2 = -2h/b

               m1 + m2 = -k

               -2 + m2 = -k

               m2 = -k + 2

• So now, we have m1 x m2 = a / b

               (-2) x (-k + 2) = 6

               2k - 4 = 6

               2k = 10

               k = 5

Answer:

               So the value of k is 5.