The red section forms an ellipse!The red cross-section forms a hyperbola, but the blue does not? It forms a parabola instead? They are two different animals?
The red section forms an ellipse!The red cross-section forms a hyperbola, but the blue does not? It forms a parabola instead? They are two different animals?
You were too quick! I saw the error right away and corrected the pic.The red section forms an ellipse!
∞-1 is not defined. You can't use infinity in arithmetic computations.I would have thought that a hyperbola with E=∞ would be the same animal as a hyperbola with E=∞-1.
Nor am I doing so. I am conceptualizing an arbitrarily large number.You can't use infinity in arithmetic computations.
Actually, you did use ∞ in an arithmetic expression. You wrote E=∞-1 in post #27, to which I replied that ∞ - 1 is meaningless, as is any arithmetic expression involving the symbol ∞.Nor am I doing so. I am conceptualizing an arbitrarily large number.
But all you need to say is that the eccentricity is greater than 1.DaveC426913 said:You must grant that a hyperbola can have an eccentricity of an arbitrarily large value - there is no value on the real number line greater than 1 that a hyperbola cannot have as its eccentricity. Literally, anything shy of infinity.