Question

Find the constant difference for a hyperbola with foci at F1 (-29, 0) and F2 (29, 0), and point on the hyperbola (21, 0).
42
36
39
45?

Answer 1

not sure what you mean by constant difference?

Answer 2

the point (21,0) must be a vertex
so
a = 21
c = 29

b = sqrt(29^2 - 21^2) = 20
hyperbola:
\[\frac{x^{2}}{21^{2}} -\frac{y^{2}}{20^{2}} = 1\]

Answer 3

the foci are defined such that the difference between distances from any point and each foci is 2a

2a = 42