Question

Find the separate equation of the lines represented by the following equation:
(i) $3y^2+7xy=0$
(ii) $5x^2-9y^2=0$
(iii) $x^2-4xy=0$
(iv) $3x^2-10xy-8y^2=0$

Answer 1

$\left(i\right)y(3y+7x)=0$

The seperate equations are $y=0,3y+7x=0$

$\left(ii\right)5x^2-9y^2=0$

$={\left(\sqrt{5}x\right)}^2-{\left(3y\right)}^2=0$

$=(\sqrt{5}x+3y)(\sqrt{5}x-3y)=0$

The seperate equations are $\sqrt{5}x+3y=0,\sqrt{5}x-3y=0$

$\left(iii\right)x^2-4xy=0$

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

The seperate equations are $x=0,x-4y=0$

$\left(iv\right)3x^2-10xy-8y^2=0$

$3x^2-12xy+2xy-8y^2=0$

$3x(x-4y)+2y(x-4y)=0$

$(x-4y)(3x+2y)=0$

The seperate equations are $x-4y=0,3x+2y=0$