Question

determine a equacao do lugar geometrico dos pontos equidistantes as retas 3x-4y= 0 e 3x-4y-4=0

Answer 1

Sendo equidistantes os pontos, devemos ter:$\frac{ \left|\begin{array}{ccc}3x-4y\\\end{array}\right| }{ \sqrt{3^2+(-4)^2} } = \frac{ \left|\begin{array}{ccc}3x-4y-4\\\end{array}\right|}{ \sqrt{3^2+(-4)^2} } \\ \frac{|3x-4y|}{5} = \frac{|3x-4y-4|}{5} \\ \\ 3x-4y=3x-4y-4=\ \textgreater \ 0=-4 \\ 3x-4y=-3x+4y+4 \\ 6x-8y-4=0 \\ 3x-4y-2=0$