Question

Find k if the slope of the lines given by
kx^2 + 4xy - y^2 = 0 is 3 times the other.​

Answer 1

The value of k is (- 3).

Step-by-step explanation:

Let the two lines be

y - mx = 0 ..... (1)

y - 3mx = 0 ..... (2)

[ Since the given pair of equations has no linear term, we omit the constant terms from (1) and (2). ]

Then the lines (1) and (2) can be written in pair as

(y - mx) (y - 3mx) = 0

or, y² - 3mxy - mxy + 3m²x² = 0

or, y² - 4mxy + 3m²x² = 0

or, - 3m²x² + 4mxy - y² = 0 ..... (3)

The given pair of lines is

kx² + 4xy - y² = 0 ..... (4)

Equating (3) and (4), we get

k = - 3m² ..... (5)

m = 1

Putting m = 1, from (5), we get

k = - 3 (1)²

i.e., k = - 3