Question

The value of ‘$c$’ such that the line joining $(0,3),(5,–2)$ is a tangent to $y=\frac{c}{x+1}$ is

• A. $-4$
• B. $4$
• C. $2$
• D. $16$

Answer 1

The correct option is B $4$

Equation of line passing through
$(0,3),(5,–2)$ is $x+y=3$
Now equating the line with given curve
$(x+1)(3–x)=c$
$\Rightarrow x^2-2x-3=-c$
$\Rightarrow x^2–2x+c–3=0$
Now for tangency
$D=0$
$\Rightarrow 4-4(c-3)=0$
$\Rightarrow c=4$