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$If the slope of one of the lines represented by a x^{2} + 2 h x y + b y^{2} = 0 is the square of the other, then \frac{a + b}{h} + \frac{8 h^{2}}{a b} =$

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Correct option is B

Let m and m2 be the slopes of the lines represented by ax2+2hxy+by2=0. Then, m+m2=−2hb and mm2=ab or m3=ab∴ m+m23=−2hb3∴ m3+m6+3mm2m+m2=−8h3b3ab+ab2+3ab-2hb=−8h3b3∴ ab2(a+b)+8h3b3=6ahb2Multiply both sides by b2ah∴ a+bh+8h2ab=6

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If the slope of one of the lines represented by ax2+2hxy+by2=0 is the square of the other, then a+bh+8h2ab=

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Ready to Test Your Skills?

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$If the slope of one of the lines represented by a x^{2} + 2 h x y + b y^{2} = 0 is the square of the other, then \frac{a + b}{h} + \frac{8 h^{2}}{a b} =$