First slide

Equation of line in Straight lines

Question

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

Moderate

A

(1,1)
B

(1,-2)
C

(-1,2)
D

(-1,1)

Solution

$a - 2 \sqrt{b c} = b + c$
$\Rightarrow {(\sqrt{b} + \sqrt{c})}^{2} - {(\sqrt{a})}^{2} = 0$ or $\sqrt{b} + \sqrt{c} - \sqrt{a} = 0$ $(∵ \sqrt{b} + \sqrt{c} + \sqrt{a} \neq 0)$
$∴ \sqrt{a} x + \sqrt{b} y + \sqrt{c}$ passes through the fixed point (-1, 1)

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