Values of m , for which the line y = m x + 2 5 is a tangent to the hyperbola 16 x 2 - 9 y 2 = 144 , are the roots of the equation x 2 - a + b x - 4 = 0 , then the value of a + b is equal to

Question

Values of m , for which the line y = m x + 2 5 is a tangent to the hyperbola 16 x 2 - 9 y 2 = 144 , are the roots of the equation x 2 - a + b x - 4 = 0 , then the value of a + b is equal to,

MARKS App · Accepted Answer

Equation of hyperbola is x 2 9 - y 2 16 = 1 . Equation of tangent is y = m x + 9 m 2 - 16 ⇒ 9 m 2 - 16 = 2 5 ⇒ m = ± 2 ⇒ a + b = sum of roots = 0 .

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