If ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pa | vedclass

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(B) The general second-degree equation $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of parallel lines if $h^2=ab$ and $bg^2=af^2$.From $h^2=ab$,we h

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$\sqrt{\frac{a}{b}}$

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(B) The general second-degree equation $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of parallel lines if $h^2=ab$ and $bg^2=af^2$.From $h^2=ab$,we have $h=\sqrt{ab}$.From $bg^2=af^2$,we can write $\frac{g^2}{f^2}=\frac{a}{b}$.For parallel lines,the condition is $\frac{a}{h}=\frac{h}{b}=\frac{g}{f}$.Thus,$\frac{g^2}{f^2}=\frac{a^2}{h^2}=\frac{a^2}{ab}=\frac{a}{b}$.Also,for parallel lines,the distance between them is given by $2\sqrt{\frac{g^2-ac}{a(a+b)}} = 2\sqrt{\frac{f^2-bc}{b(a+b)}}$.This implies $\frac{g^2-ac}{a} = \frac{f^2-bc}{b}$.Therefore,$\frac{g^2-ac}{f^2-bc} = \frac{a}{b}$.Taking the square root on both sides,we get $\sqrt{\frac{g^2-ac}{f^2-bc}} = \sqrt{\frac{a}{b}}$.

If $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of parallel lines,then $\sqrt{\frac{g^2-ac}{f^2-bc}}$ is equal to

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