if sum of the slopes of the lines given by 4x2-2IkIxy-7y2=0 is equal to the product of the slopes then k=

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Solution

Dear student,

Given that the sum of the slopes of the lines given by 4x²-2kxy-7y² = 0 is equal to the product of the slopes
Compare 4x²-2kxy-7y² = 0 with ax²+ 2bxy+cy² = 0

Sum of slopes = $\frac{- 2 b}{c}$
Product of slopes = $\frac{a}{c}$
Given that
Sum of slopes = Product of slopes
=> $\frac{- 2 b}{c}$ = $\frac{a}{c}$
$- \frac{(- 2 k)}{(- 7)} = \frac{1}{(- 7)} = > - \frac{2 k}{7} = - \frac{1}{7} = > 2 k = 1 = > k = \frac{1}{2}$

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