Question

Find the constant difference for a hyperbola with foci F1 (-8, 0) and F2 (8, 0) and the point on the hyperbola (8, 30). The constant difference is: ____. Enter only a number.

Answer 1

The distance formula can be used to determine the constant difference of the hyperbola. So,
2a = | (√( (x - c)² + y² ) - √( (x + c)² + y² ) |
where
2a is the constant difference
(x,y) is the point on the parabola = (8,30)
c is the distance from the center to the focus = 8

Plugging in the given values
2a = | √( (8 - 8)² + 30² ) - √( (8 + 8)² + 30² )
2a = 4

Therefore, the constant difference is 4.