The slope of one line is double the slope of another line in the combined equation of the pair of linesx2a+2xyh+y2b=0. If the value of ab:h2=k:l then k+l=_____ (where k,l are coprimes)

If m and 2m are the slopes thenm+2m=−2/h1b=−2bhAnd m x 2m=1a1b=baEliminating m, we get2−2b3h2=baabh2=98ab:h2=98

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The slope of one line is double the slope of another line in the combined equation of the pair of lines $\frac{x^{2}}{a} + \frac{2 x y}{h} + \frac{y^{2}}{b} = 0$ . If the value of $a b : h^{2} = k : l t h e n k + l =_____(w h e r e k, l a r e c o p r i m e s)$

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If m and 2m are the slopes then
$m + 2 m = \frac{- 2 / h}{\frac{1}{b}} = \frac{- 2 b}{h}$

And $m x 2m= \frac{\frac{1}{a}}{\frac{1}{b}} = \frac{b}{a}$

Eliminating m, we get

$\begin{array}{l} 2 {(- \frac{2 b}{3 h})}^{2} = \frac{b}{a} \\ \frac{a b}{h^{2}} = \frac{9}{8} \\ a b : h^{2} = \frac{9}{8} \end{array}$

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