Sector Command

Sector( <Conic>, <Point>, <Point> )

Yields a conic sector between two points on the conic section and calculates its area.

  • Let c: x^2 + 2y^2 = 8 be an ellipse, D = (-2.83, 0) and E = (0, -2) two points on the ellipse. Sector(c, D, E) yields d = 4.44.

  • Let c: x^2 + y^2 = 9 be a circle, A = (3, 0) and B = (0, 3) two points on the circle. Sector(c, A, B) yields d = 7.07

This works only for a circle or ellipse.
Sector( <Conic>, <Parameter Value>, <Parameter Value> )

Yields a conic sector between two parameter values between 0 and 2π on the conic section and calculates its area.

Let c: x^2 + y^2 = 9 be a circle. Sector(c, 0, 3/4 π) yields d = 10.6

Internally the following parametric forms are used:

  • Circle: (r cos(t), r sin(t)) where r is the circle’s radius.

  • Ellipse: (a cos(t), b sin(t)) where a and b are the lengths of the semimajor and semiminor axes.