The lines represented by the equation x^2-y^2 | vedclass

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(D) The given equation is $x^2-y^2-x+3y-2=0$. We can rearrange the terms as $x^2 - (y^2 - 3y + 2) - x = 0$. Factoring the quadratic in $y$: $y^2 - 3y

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$x-y+1=0, x+y-2=0$

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(D) The given equation is $x^2-y^2-x+3y-2=0$. We can rearrange the terms as $x^2 - (y^2 - 3y + 2) - x = 0$. Factoring the quadratic in $y$: $y^2 - 3y + 2 = (y-1)(y-2)$. To factor the whole expression,we look for factors of the form $(x+ay+b)(x+cy+d)$. Expanding $(x-y+1)(x+y-2) = x^2 + xy - 2x - xy - y^2 + 2y + x + y - 2 = x^2 - y^2 - x + 3y - 2$. Thus,the equation represents the lines $x-y+1=0$ and $x+y-2=0$.

The lines represented by the equation $x^2-y^2-x+3y-2=0$ are :

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