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JEE Main202124 Feb 2021Evening ShiftMathematicsApplication of DerivativesActual

If the curve y = a x 2 + b x + c , x ∈ R , passes through the point 1 , 2 and the tangent line to this curve at origin is y = x , then the possible values of a , b , c are:

Options

  1. Aa = - 1 ,   b = 1 ,   c = 1
  2. Ba = 1 ,   b = 0 ,   c = 1
  3. Ca = 1 ,   b = 1 ,   c = 0
  4. Da = 1 2 , b = 1 2 , c = 1

Correct answer

C. a = 1 ,   b = 1 ,   c = 0

Step-by-step solution

a + b + c = 2   … 1 and d y d x | 0 ,   0 = 1 2 a x + b | 0 ,   0 = 1 b = 1 Curve passes through origin So, c = 0 and a = 1

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