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AP EAMCET202315 May 2023Evening ShiftMathematicsApplication of DerivativesActual

If the points of contact of the tangents drawn from (0,0) to the curve y=x^2+3 x+4 are ( , ) and ( , ) , then + =

Options

  1. A7
  2. B25
  3. C16
  4. D13

Correct answer

C. 16

Step-by-step solution

Given y=x^2+3 x+4 Now d y d x =2 x+3 At (h, k) . d y d x |_ (h, k) =2 h+3 So, equation of tangent at (h, k) y-k=(2 h+3)(x-h) It is passes through (0,0) So -k=(2 h+3)(-h) k=2 h^2+3 k...(i) and k=h^2+3 h+4...(ii) After solving (i) & (ii), we get aligned & (h, k)=(-2,2) or (2,14) & so ( , )=(-2,2) & ( , )=(2,14) & + =2+14=16 aligned

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