AP EAMCET202419 May 2024Evening ShiftMathematicsApplication of DerivativesActual

If the equation of tangent at (2,3) on y^2=a x^3+b is y=4 x-5 , then the value of a^2+b^2=

Options

Correct answer

B. 53

Step-by-step solution

Given the curve, y^2=a x^3+b 2 y d y d x =3 a x^2 d y d x = 3 a x^2 2 y at (2,3) , d y d x = 12 a 6 =2 a Since, slope of tangent to the line y=4 x-5 is 4 aligned & So, 2 a=4 a=2 & b=9-16=-7 a^2+b^2=49+4=53 aligned

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