Question

The point on the hyperbola $y=\frac{x-1}{x+1}$ at which the tangents are parallel to $y=2x+1$ are

• A. $(0,-1)$ only
• B. $(-2,3)$ only
• C. $(0,-1),(-2,3)$
• D. $(2,3)(5,4)$

Answer 1

The correct option is C $(0,-1),(-2,3)$

Given,

$y=\frac{x+1}{x-1}$

Slope of tangent at $(x,y)=\frac{dy}{dx}=\frac{2}{(x+1{)}^2}$

for tangent to be parallel to $y=2x+1$

$\frac{2}{(x+1{)}^2}=2\Rightarrow (x+1{)}^2=1$

$\Rightarrow x=0$ or $x=-2$

$\Rightarrow$ corresponding points are $(0,-1)$ & $(-2,3)$