Question

What is the constant difference for a hyperbola with a foci f1 (- 8, 0) and F2 (8,0) and the point on the hyperbola (8, 30)

Answer 1

F1P - F2P = k ;
F1P = $\sqrt{ (-8-8)^{2} + (0-30)^{2} } = \sqrt{64 + 900} = \sqrt{964} = 31.04;$
F2P = $\sqrt{ (8-8)^{2} + (0-30)^{2} } = \sqrt{900} = 30;$
31.04 - 31 = 0.04 => k = 0.04 ;