Question

Find k if the slope of the lines given by kx2+ 4xy - y2 = 0 is 3 times the other.​

Answer 1

value of k = -3

slope of lines given by kx² + 4xy - y² = 0 is three times of the other.

kx² + 4xy - y² = 0 is a homogeneous equation of lines means both the line is passing through origin.

let m is slope of one line then 3m shall be the slope of the other line.

then equations of lines are y = mx and y = 3mx

so, (mx - y)(3mx - y ) = kx² + 4xy - y²

⇒3m²x² - 4mxy + y² = kx² + 4xy - y²

⇒-1(-3m²x² + 4mxy - y²) = kx² + 4xy - y²

on comparing we get,

k = -3m², 4m = 4 ⇒m = 1

so, k = -3(1)² = -3

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Answer 2

Answer:

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Step-by-step explanation:

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