AP EAMCET202422 May 2024Evening ShiftMathematicsApplication of DerivativesActual

If the curves 2 x^2+k y^2=30 and 3 y^2=28 x cut each other orthogonally, then k=

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Correct answer

D. 1

Step-by-step solution

2 x^2+k y^2=30 ...(i) 4 x+2 k y d y d x =0 d y d x = -2 x k y =m₁ And 3 y^2=28 x ...(ii) 6 y d y d x =28 d y d x = 14 3 y =m₂ Since, curves cut orthogonally aligned & m₁ m₂=-1 -2 x k y 14 3 y =-1 & k= 28 x 3 y^2 =1 aligned [From (ii)]

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