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Find k, if the sum of the slopes of the lines represented by x2 + kxy − 3y2 = 0 is twice their product. - Mathematics and Statistics

Sum

Find k, if the sum of the slopes of the lines represented by x2 + kxy − 3y2 = 0 is twice their product. 

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Solution

Comparing the equation x2 + kxy − 3y2 = 0 with ax2 + 2hxy − by2 = 0,

We get, a = 1, 2h = k, b = −3.

Let m1 and m2 be the slopes of the lines represented by x2 + kxy − 3y2 = 0 

∴ m1 + m2 = `(-2"h")/"b" = - "k"/(-3) = "k"/3`

And m1m2 = `"a"/"b" = 1/(-3) = - 1/3`

Now, m1 + m2 = 2(m1m2)    .......(Given)

∴ `"k"/3 = 2(- 1/3)`

∴ k = − 2.

Concept: Homogeneous Equation of Degree Two
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