Question

Choose correct alternatives:

If two lines ax² + 2hxy + by² = 0 make angles α and β with X-axis, then tan (α + β) = _____.

पर्याय

• `"h"/("a + b")`

• `"h"/("a - b")`

• `"2h"/("a + b")`

• `"2h"/("a - b")`

Answer 1

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")`