Tangents to curves in the plane

### 25.6.7 Tangents to curves in the plane

See Section 26.5.3 for tangents in space.

The tangent command finds tangents to curves.

- tangent takes one or two arguments:
  - C, a curve.
  - p, a point.
  or
  - e, a point defined with element (see Section 25.5.15) using a curve and parameter value.
- tangent(C,p) (or tangent(e)) returns and draws the list of lines tangent to the curve passing through the given point.

#### Examples

C:=circle(0,1,color=blue); T:=tangent(C,3+2i,color=orange)

purge(t):; t:=element(0..pi,pi/3):; C:=circle(0,1,color=blue); A:=element(C,t); T:=tangent(A,color=orange)

When tangent is called with an element, the tangent will change along with the point on the element.