$x^2-6xy+8y^2=0$
$(x^2-6xy+9y^2)-y^2=0$
$(x-3y{)}^2-y^2=0$
(x − 3y − y)(x − 3y + y) = 0
(x − 4y)(x − 2y) = 0
x − 4y = 0
4y = x
$y=\frac{1}{4}x$

или
x − 2y = 0
2y = x
$y=\frac{1}{2}x$

$2x^2+5xy+2y^2=0$
$2x^2+4xy+xy+2y^2=0$
$(2x^2+4xy)+(xy+2y^2)=$
$2x(x+2y)+y(x+2y)=0$
(x + 2y)(2x + y) = 0
x + 2y = 0
2y = −x
$y=-\frac{1}{2}x$

2x + y = 0
y = −2x

$x^2+xy-2y^2=0$
$x^2+xy-y^2-y^2=0$
$(x^2-y^2)+(xy-y^2)=0$
(x − y)(x + y) + y(x − y) = 0
(x − y)(x + y + y) = 0
(x − y)(x + 2y) = 0
x − y = 0
y = x

или
x + 2y = 0
2y = −x
$y=-\frac{1}{2}x$

$3x^2-10xy+3y^2=0$
$3x^2+6x^2-10xy-2xy+3y^2+y^2-6x^2+2xy-y^2=0$
$(9x^2-12xy+4y^2)-(6x^2-2xy)-y^2=0$
$(3x-2y{)}^2-2x(3x-y)-y^2=0$
$((3x-2y{)}^2-y^2)-2x(3x-y)=0$
(3x − 2y − y)(3x − 2y + y) − 2x(3x − y) = 0
(3x − 3y)(3x − y) − 2x(3x − y) = 0
(3x − y)(3x − 3y − 2x) = 0
(3x − y)(x − 3y) = 0
3x − y = 0
y = 3x

или
x − 3y = 0
3y = x
$y=\frac{x}{3}$