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BITSAT 2017

Exam: BITSAT
Year: 2017
Subject: Mathematics
Chapter: Application of Derivatives

BITSAT 2017 · Mathematics · Application of Derivatives

Line joining the points (0,3) and ( 5, - 2 ) is a tangent to the...

Line joining the points

(0,3)

and

( 5, - 2 )

is a tangent to the curve

y = \dfrac{ax}{1 + x}

, then

Options

A $a = 1 \pm \sqrt{3}$
B $a \in ϕ$
C $a = - 1 \pm \sqrt{3}$
D $a = - 2 \pm 2\sqrt{3}$

Correct answer

B. $a \in ϕ$

Step-by-step solution

Equation of line joining the points $(0,3)$ and $( 5, - 2 )$ is $y = 3 - x$ .

If this line is tangent to $y = \dfrac{ax}{( x + 1 )}$ , then

$( 3 - x ) ( x + 1 ) = ax$ should have equal roots.

Thus, $( a - 2{)}^{2} + 12 = 0$

$⇒$ No value of $a ⇒ a \in ϕ$

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