### 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