Question

The equation of tangent to the curve $y=\frac{x+9}{x+5}$ so that is passes through the origin is

• A. $x+y=0$
• B. $x-y=0$
• C. $x+y=1$
• D. $x-y=1$

Answer 1

The correct option is A $x+y=0$

Equation of tangent of $y$ $=$ $\frac{x+9}{x+5}$ that passes through again be $y=mx$

$\frac{dy}{dx}=\frac{-4}{(x+5{)}^2}$

Value of $dy/dx$ should be as the $m$ or $y/x$ at that point ($x_1,y_1$)

$\frac{-4}{(x_1+5{)}^2}=\frac{y_1}{x_1}$

$\frac{-4}{(x_1+5{)}^2}=\frac{(x_1+9}{(x_1+5)\left(x_1\right)}$

$x_1^2+18x+45=0$

$x_1=-3$

$y_1=3$

$m=\frac{y_1}{x_1}=\frac{-3}{-3}=-1$

Tangent $\to y=-x$

$x+y=0$