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MHT CET202519 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

If two curves x^2-4 y^2=2 and 8 x^2=40- my ^2 are orthogonal to each other then m =

Options

  1. A2
  2. B16
  3. C1 2
  4. D4

Correct answer

B. 16

Step-by-step solution

Orthogonal Curves Condition Two curves are orthogonal if their tangent slopes at intersection points satisfy m₁ m₂ = -1 . The first curve x^2 - 4y^2 = 2 has derivative 2x - 8y dy dx = 0 , yielding slope dy dx = x 4y . The second curve 8x^2 = 40 - my^2 differentiates to 16x = -2my dy dx , giving slope dy dx = - 8x my . Setting the product of slopes equal to -1 : ( x 4y ) (- 8x my ) = -1 Simplifying yields 2x^2 my^2 = 1 , or 2x^2 = my^2 . Substituting into the second original equation: 8x^2 = 40 - 2x^2 10x^2 = 40 x^2

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