Orthogonal Trajectories

Enter a formula giving y as a function of x and c. Click on the graph to draw "level curves" of that function (graphs for a particular value of c). Choose "orthogonal trajectories" to draw orthogonal (perpendicular) curves.

Try copying the following formulas into the applet. (In some cases, the corresponding orthogonal families are given in brackets.)

y = c*x [x² + y² = c] y = c*exp(x) [y² = x + c]

y = c-x^2/2 [y = ln(x) + c] y = c-x^3/3-x [y = arctan(x) + c]

y = c-x^4/4-x^2/2 [y = ln(x/sqrt(1+x^2)) + c] y = c*tan(x)^(1/3)

y = c*x^3+x y = x^3+c*x

y = x*(x+c) y = c/x [x² – y² = c]

y = c/(x^2+1) [2y² = x² + ln(x²) + c] y = cos(x) + x + c [y = – tan(x/2) + c]

y = c*x	[x² + y² = c]	y = c*exp(x)	[y² = x + c]
y = c-x^2/2	[y = ln(x) + c]	y = c-x^3/3-x	[y = arctan(x) + c]
y = c-x^4/4-x^2/2	[y = ln(x/sqrt(1+x^2)) + c]	y = c*tan(x)^(1/3)
y = c*x^3+x		y = x^3+c*x
y = x*(x+c)		y = c/x	[x² – y² = c]
y = c/(x^2+1)	[2y² = x² + ln(x²) + c]	y = cos(x) + x + c	[y = – tan(x/2) + c]