The chord of the curve y - x 2-2 ax - b- joining the points where x - and x - is parallel to the tangent to the curve at abscissa x -A- a - b -2B- 2 a2-b-3nC- 2 -3-3RD- -2

The correct option is D α+β2Slope of tangent nbsp;=dydx=2x+2a Slope of chord =(β^2+ 2aβ + b) (α^2+ 2aα + b)β α=α+β+2a Since both are parallel nbsp; nbsp ...

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Byju's Answer

Standard XII

Mathematics

Condition for Two Lines to Be Parallel

The chord of ...

Question

The chord of the curve $y = x^{2} + 2 a x + b$ , joining the points where $x = α$ and $x = β$ , is parallel to the tangent to the curve at abscissa $x =$

\frac{a + b}{2}

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\frac{2 a + b}{3}

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\frac{2 α + β}{3}

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\frac{α + β}{2}

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Solution

The correct option is D $\frac{α + β}{2}$
Slope of tangent
$= \frac{d y}{d x} = 2 x + 2 a$
Slope of chord
$= \frac{(β^{2} + 2 a β + b) - (α^{2} + 2 a α + b)}{β - α} = α + β + 2 a$
Since both are parallel
$\Rightarrow 2 x + 2 a = α + β + 2 a x = \frac{α + β}{2}$

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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=

The correct option is D α+β2Slope of tangent =dydx=2x+2a Slope of chord =(β2+2aβ+b)−(α2+2aα+b)β−α=α+β+2a Since both are parallel ⇒2x+2a=α+β+2ax=α+β2

The chord of the curve $y = x^{2} + 2 a x + b$ , joining the points where $x = α$ and $x = β$ , is parallel to the tangent to the curve at abscissa $x =$

The correct option is D $\frac{α + β}{2}$
Slope of tangent
$= \frac{d y}{d x} = 2 x + 2 a$
Slope of chord
$= \frac{(β^{2} + 2 a β + b) - (α^{2} + 2 a α + b)}{β - α} = α + β + 2 a$
Since both are parallel
$\Rightarrow 2 x + 2 a = α + β + 2 a x = \frac{α + β}{2}$