Question

The equation of the line passing through origin which is parallel to the tangent of the curve $y=\dfrac{x-2}{x-3}$ at $x=4$ is

• A. $y=2x$
• B. $y=-2x+1$
• C. $y=-x$
• D. $y=x+2$
• E. $y=4x$

Answer 1

Answer: (C)

$y=-x$

Answer 2

$y=\dfrac{x-3}{x-2}$

$⇒\dfrac{dy}{dx}=\dfrac{(x-3).1-(x-2).1}{(x-3)^2}$

$⇒\dfrac{dy}{dx}=\dfrac{-1}{(x-3)^2}$

Then ⇒$\dfrac{dy}{dx}$ at $x=4$ $=\dfrac{-1}{(4-3)^2}$

                                $=-1$

means the slope$=-1$

Therefore,the equation of the line passing through origin which is parallel to the tangent of the curve $y=\dfrac{x-2}{x-3}$ at $x=4$ is

$y=-x$ (_Ans)