If abc−2=b/c+c/b , where a,b,c>0 , then the family of lines ax+by+c=0 passes through the fixed point is (x,y) then y−x=

abc−2=bc+cbor a=b+c+2bcor a=(b+c)2or a−b−c=0since a+b+c≠0(as a,b,c>0)Comparing ax+by+c=0 , we have x=−1,y=1

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If $\frac{a}{\sqrt{b c}} - 2 = \sqrt{b / c} + \sqrt{c / b}$ , where $a, b, c > 0$ , then the family of lines $\sqrt{a} x + \sqrt{b} y + \sqrt{c} = 0$ passes through the fixed point is $(x, y)$ then $y - x =$

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Detailed Solution

$\frac{a}{\sqrt{b c}} - 2 = \sqrt{\frac{b}{c}} + \sqrt{\frac{c}{b}}$
or $a = b + c + 2 \sqrt{b c}$
or $a = {(\sqrt{b} + \sqrt{c})}^{2}$
or $\sqrt{a} - \sqrt{b} - \sqrt{c} = 0$
since $\sqrt{a} + \sqrt{b} + \sqrt{c} \neq 0 (a s a, b, c > 0)$
Comparing $\sqrt{a} x + \sqrt{b} y + \sqrt{c} = 0$ , we have $x = - 1, y = 1$

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