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MHT CET2010MathematicsApplication of Derivatives

The equation of tangent to the curve y²=a x²+b at point (2,3) is y=4 x-5 , then the values of a and b are

Options

  1. A3,-5
  2. B6,-5
  3. C6,15
  4. D6,-15

Correct answer

D. 6,-15

Step-by-step solution

Given, y²=a x²+b² 2 y d y d x =2 a x d y d x = a x y Slope at (2,3)= ( d y d x )_ (2,3) = 2 a 3 But slope of given tangent is m=4 2 a 3 =4 a =6 Since, point (2,3) lies on the curve so, it satisfies the equation of the curve (3)²=6(2)²+b b=-15

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