Choose correct alternatives: If two lines ax2 + 2hxy + by2 = 0 make angles $\alpha$ and $\beta$ with X-axis, then tan ($\alpha$ + $\beta$) = _____.

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KollegeApply · Accepted Answer

If two lines ax2 + 2hxy + by2 = 0 make angles $\alpha$ and $\beta$ with X-axis, then tan ($\alpha$ + $\beta$) = "2h"/("a - b") Explanation: m1 = tan $\alpha$, m2 = tan $\beta$ $\therefore$ tan ($\alpha$ + $\beta$) = `("tan" alpha + "tan" beta)/(1 - "tan" alpha*"tan" beta) = ("m"_1 + "m"_2)/(1 - "m"_1"m"_2) = (- 2"h"//"b")/(1 - ("a"//"b")) = "2h"/("a" - "b")`

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