Question

What curve (or curves) does the equation $x^2-5xy+4y^2=0$ represent ?

Answer 1

let solve the equation first,

$x^2-5xy+4y^2=0$

$x^2-4xy-xy+4y^2=0$

$x(x-4y)-y(x-4y)=0$

$(x-y)(x-4y)=0$

$\to x=y$

$\to x=4y$

there are two linear equation formed by the equation

so these two lines or curves represent the

eqautaion $x^2-5xy+4y^2=0$