Question

URGENT PLEASE

Identify the constant difference for a hyperbola with foci (−3, 0) and (3, 0) and a point on the hyperbola (7, 0).

Answer 1

6

Explanation:

By definition, the constant difference for a hyperbola is:

d = |PF1 - PF2|

where PF1 is the distance between points P and F1, and PF2 is the distance between points P and F2

Let's call F1 to (-3, 0), F2 to (3, 0) and P (7, 0). Then, the distances are:

PF1 = √[(-3 - 4)² + (0 - 0)²] = 7

PF2 = √[(3 - 4)² + (0 - 0)²] = 1

And the the constant difference is:

d = |7 - 1| = 6