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Question

The chord of the curve y=x2+2ax+b, joining the points where x=α and x=β, is parallel to the tangent to the curve at abscissa x=
  1. a+b2
  2. 2a+b3
  3. 2α+β3
  4. α+β2


Solution

The correct option is D α+β2
Slope of tangent
 =dydx=2x+2a
Slope of chord
=(β2+2aβ+b)(α2+2aα+b)βα=α+β+2a
Since both are parallel  
2x+2a=α+β+2ax=α+β2

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