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MHT CET202020 Oct 2020Morning ShiftMathematicsApplication of DerivativesActual

If the line y=4 x-5 touches the curve y²=a x³+b at the point (2,3) , then

Options

  1. Aa=-2, b=-7
  2. Ba=-2, b=7
  3. Ca=2 , b=-7
  4. Da=2, b=7

Correct answer

C. a=2 , b=-7

Step-by-step solution

Line y=4 x-5 has slope 4 We have y²=a x³+b 2 y d y d x =3 a x² array l dy d x = 3 ax ² 2 y ( dy dx )_ (2,3) = 3 a (2)² 2(3) =2 a array As per given condition, 2 a =4 a =2 Now y²=a x³+b at point (2,3) becomes 9=8(2)+b b=-7 This problem can be alternatively solved as follows: Put y=4 x-5 in y²=a x³+b (4 x-5)²=a x³+b When x=2 , we get 9=8 a+b (1) Now we will go by options Put a =2, ~b =-7 in equation (1) we get 8(a)-7=16-7=9

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