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Mathematics Test 89

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Mathematics Test 89
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  • Question 1
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    If the line y = 3x + λ touches the hyperbola 9x2 – 5y2 = 45, then the value of λ is-

    Solution

    Equation of hyperbola can be written as

     x2/5 - y2/9 = 1

    & straight line y = 3x + l is a tangent of hyperbola.

    By the condition of tangency

    c2 = a2m2 - b2

    ⇒ λ2 = 5(9) – 9

    ⇒ λ2 = 36

    ⇒ λ = ±6

     

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