# Tangent lines

Can someone help me with this problem?

Consider the curve defined by y=x/(x+1). (1,2) is a point NOT on the curve.
Find the equations of the two tangent lines to the curve passing through the point
(1,2).

djeitnstine
Gold Member
There are some ways to attack this problem but my first instinct is to sketch or print the graph then mark the point (1,2) then take a ruler and carefully draw the tangent lines touching one point on each side of the graph. Then take the derivative around those points and use the formula of a line (y=mx+c) and check to see if the gradients run through the points.

This is perhaps tedious to say the least but I don't know how else to tackle the problem without any more information.

btw winplot should help with this.

tiny-tim
Homework Helper
hihi davedave!

Write y = ax + b for a typical line.

What is the restriction on a and b for it to pass through (1,2)?

Now find the equation for the points of intersection of that line with y=x/(x+1).

That should be a quadratic equation.

What is the condition for that equation to have two equal roots?