Orthogonal

Family — Orthogonal trajectories —

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The perpendicularity check appears here after a simulation.

Steps derived by the program

1Type of equation

Explicit
y = f(x, c) Implicit
F(x, y, c) = 0

Explicit: y alone on the left. Implicit: any equation with x, y and c.

2Equation of the family

Use x, y, the parameter, numbers, + − * / ^ ( ), pi, e and sin, cos, tan, exp, ln, sqrt. Write 2x for 2·x.

3Name of the parameter

One letter (usually c or k), not x, y or e.

4Values of the parameter

A range such as -3 to 3, or a list such as 1, 2, 4.

5Number of curves (for a range)

1 to 40 curves, evenly spaced over the range.

6View range

x min

x max

y min

y max

The graph keeps equal scales on both axes, so the shorter side is widened to fit the screen.

7Number of orthogonal curves

1 to 60 trajectories (optional, default 12).

8Colours (optional)

Family Trajectories

Examples — click to fill the form