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 ...

You visited us 9 times! Enjoying our articles? Unlock Full Access!

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}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2 a + b}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2 α + β}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{α + β}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

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
$\Rightarrow 2 x + 2 a = α + β + 2 a x = \frac{α + β}{2}$

Suggest Corrections

Similar questions

Q. 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 =

Q. lf the chord joining the points where

x = p, x = q

on the curve

y = a x^{2} + b x + c

is parallel to the tangent drawn to the curve at

(α, β)

then

α =

The chord joining the points where x =p and x=q on the curve $y = a x^{2} + b x + c$ is parallel to the tangent at the point on the curve whose abscissa is

Q. If the tangent to the curve

y = \frac{x}{x^{2} - 3}, x \in R, (x \neq \pm \sqrt{3},)

at a point

(α, β) \neq (0, 0)

on it is parallel to the line

2 x + 6 y - 11 = 0,

then :

Q. If the tangent to the curve

y = \frac{x}{x^{2} - 3}, x \in R, (x \neq \pm \sqrt{3},)

at a point

(α, β) \neq (0, 0)

is parallel to the line

2 x + 6 y - 11 = 0,

then

| 6 α + 2 β | =

Join BYJU'S Learning Program

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
$\Rightarrow 2 x + 2 a = α + β + 2 a x = \frac{α + β}{2}$