### 18.2.2 Osculating circle of a curve

The osculating_circle command finds and draws the osculating circle of a curve.

- To find the osculating circle from a parameterization, osculating_circle takes three arguments:
  - C, a curve.
  - t, the parameter of the curve.
  - t0, a value of the parameter.
- osculating_circle(C,t,t0) draws and returns the osculating circle of the curve at the point specified by t0.
- To find the osculating circle from a curve object, osculating_circle takes two arguments:
  - C, a curve.
  - p, a point on the curve.
- osculating_circle(C,p) draws and returns the osculating circle of C at the point p.

#### Examples

osculating_circle(plot(x^2),point(1,1))

equation(osculating_circle(plot(x^2),point(1,1)))

| ⎛ ⎝ | x+4 | ⎞ ⎠ | 2+ | ⎛ ⎜ ⎜ ⎝ | y− |
7
2
| ⎞ ⎟ ⎟ ⎠ |
2
| = |
125
4

equation(osculating_circle([t^2,t^3],t,1))

| ⎛ ⎜ ⎜ ⎝ | x+ |
11
2
| ⎞ ⎟ ⎟ ⎠ |
2
| + | ⎛ ⎜ ⎜ ⎝ | y− |
16
3
| ⎞ ⎟ ⎟ ⎠ |
2
| = |
2197
36