Question

Consider again the two points F(−9, 0) and ????(9, 0) in the coordinate plane. The equation of the

hyperbola defined by |FP − PG| = k for some constant k is given by
x^2 / 25 − y^2 / 56 = 1. What is the
value of k?

Answer 1

k = 2a = 10

Explanation:

If

x² / 25 − y² / 56 = 1

we know that

a² = 25 ⇒ a = 5

b² = 256 ⇒ b = √256

The equation of the hyperbola defined by |FP − PG| = k can be written as follows:

|FP − PG| = 2*a

then

2*a = 2*5 = 10