could someone please explain "family of curves" and give me an example. thx

Question

anonymous · Answer

I'm not really sure that is "defined" in any detailed way.

I suppose it means something like curves derived from a common source exhibiting some type of shared behaviour.

Contours? Conics? Spirals? That sort of thing.

anonymous · Answer

One family of curves is the set of hyperbolas xy = a.
Another family of curves is the set of hyperbolas x^2 - y^2 = b, where a and b run through the real numbers.

anonymous · Answer

True but you can take all the conic curves together as one family.

anonymous · Answer

Family curves, eg, hyperbola; f(x)=1/x
The family of curves are different intervals of 1/x
A curve at 1, a curve at 2, etc
Picture a contour map.

anonymous · Answer

If you select a set of values for a and the same set of values for b and graph those  members from each family on the same coordinate axes, you will see that each member of one family intersects orthogonally to every member of the other family.