# Tangent through point touching function

- Author:
- Alexander Thaller

- Topic:
- Tangent Line or Tangent

## Question

You have a point with coordinates and a function . does not lie on the graph of .
What is the equation of a tangent that touches and goes through the point ?

If you use the and the function as an argument, you only get a tangent to the function at a new point that has the same coordinate and lies on the graph of . This is not what we want to achieve.
But there is a trick so we can get our tangent(s). The and then use the

``

`Tangent`

command with the point `Tangent`

command has a version with a point and an implicit function as arguments. This works as we want to. So we convert our function f(x) into an implicit equation with `Tangent`

command. Sometimes it is necessary to zoom out to get more tangents.
See the following applet