Question

If the line joining the points $(0,3)$ and $(5,-2)$ is a tangent to the curve $y=\frac{c}{x+1},$ then the value of $c$ is ?

Answer 1

Given the points

$(0,3)(5,-2)$

tangant the curve

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

We know that

$(y-y_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$x_1=0,y_1=3,x_2=5,y_2=2$

$(y-3)=\frac{-2-3}{5-0}(x-5)$

$y-3=\frac{-5}{5}(x-5)$

$y-3=-x+5$
$x+y=5+3\Rightarrow x+y=8$

$y(x+1)=c$

$xy+y=c\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\left(i\right)$

$x+y=8\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\left(ii\right)$

Compair both equation and than

$c=8$