If one of the lines given by 6x^2 - xy + 4cy^2 = 0 is 3x + 4y = 0, then c equals :

Question

If one of the lines given by $6{x^2} - xy + 4c{y^2} = 0$ is $3x + 4y = 0,$ then $c$ equals :

Accepted Answer

$3x+4y=0$ is one of the lines of the pair

$6{x^2} - xy + 4c{y^2} = 0,$  $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$

Put  $$y =  - {3 \over 4}x,$$

we get $$6{x^2} + {3 \over 4}{x^2} + 4c{\left( { - {3 \over 4}x} \right)^2} = 0$$

$$ \Rightarrow 6 + {3 \over 4} + {{9c} \over 4} = 0 \Rightarrow c =  - 3$$

Solutions · 1