what is b in the equation of hyperbola and how is it equal to sqrt(c^2-a^) ?

Question

what is b in the equation of hyperbola and how is it equal to sqrt(c^2-a^)  ?

amistre64 · Answer

b is usuallt defined as the distance to the 'ghost of the vertex' of its elliptical cousin

amistre64 · Answer

just call me webster lol

anonymous · Answer

plz elaborate

amistre64 · Answer

there is this 'box' formed by a(distance to vertex); b(distance to ghost vertex) and the diagonal c(distance to foci)

amistre64 · Answer

these three points are the same type of setup either in ellipse or hyperbola

amistre64 · Answer

attachment

amistre64 · Answer

the measure of a,b,and c form a right triangle; c = hyp; a and b are the legs

amistre64 · Answer

a^2 + b^2 = c^2  ;  b = sqrt(c^2 - a^2)

anonymous · Answer

so far as i know, c is the distance between the centre and the focus. but acc. to ur figure, c is half the given diagonal. are both the same?

amistre64 · Answer

that is correct; it just so happens, by some fluke of math prolly, that the distances measured by 'c' are the same.  the focal distance = diagonal distance between vertexes

amistre64 · Answer

it can be better proofed in an ellipse; since that is drawn as sum of the distances from each foci remains constant; at the points of vertices, the properties exhibit that phenomena.

amistre64 · Answer

this might make sense; or not :)