MathematicsIf values of m for which the line y=mx+25 touches the hyperbola 16×2-9y2=144 are roots of the equation x2-(a+b)x-4=0 , then value of (a + b) is equal to

If values of m for which the line y=mx+25 touches the hyperbola 16x2-9y2=144 are roots of the equation x2-(a+b)x-4=0 , then value of (a + b) is equal to

  1. A

    2

  2. B

    4

  3. C

    zero

  4. D

    5

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    Solution:

    Given hyperbola   16x2-9y2=144 x29-y216=1 where a2=9, b2=16 If y=mx+25 is tangent then c2=a2m2-b2 20=9m2-16 9m2=36 m2=4 m=±2 Given  equation x2-(a+b)x-4=0 Given  -2,2 are roots of this equation sum of roots = a+b -2+2=a+b a+b=0

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