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Question
Choose correct alternatives:
If two lines ax2 + 2hxy + by2 = 0 make angles α and β with X-axis, then tan (α + β) = _____.
Options
`"h"/("a + b")`
`"h"/("a - b")`
`"2h"/("a + b")`
`"2h"/("a - b")`
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Solution
If two lines ax2 + 2hxy + by2 = 0 make angles α and β with X-axis, then tan (α + β) = `"2h"/("a - b")`
Explanation:
m1 = tan α, m2 = tan β
∴ tan (α + β) = `("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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