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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=

A
a+b2
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B
2a+b3
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C
2α+β3
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D
α+β2
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Solution

The correct option is D α+β2
Given curve is y=x2+2ax+b
Differentiate above equation w.r.t. x we get
dydx=2x+2a is the equation of tangent to the curve
But tangent to the curve is parallel to the chord of the curve which joins the points x=α and x=β
Tangent to this curve is =(α+β)+2a
2x+2a=(β+α)+2a
x=α+β2

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