Carol H. answered • 09/15/17

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25(y-4)

^{2}- 16(x-3)^{2}= 400 Divide both sides of the equation by 400.(y-4)

^{2}/16 - (x-3)^{2}/25 = 1 The center is at (3,4). This is the equation of a hyperbola, which opens up and down.a

^{2}= 16, a = ±4 b^{2}= 25, b = ±5c

^{2}= a^{2}+ b^{2}c^{2}= 4^{2}+ 5^{2}= 16 + 25 = 41c = ±√41 ≈ ±6.4

a = the distance between the center and the vertex.

V(3,8) V'(3,0)

c = the distance between the center and the focus.

F(3, 10.4) F'(3, -2.4)

Hyperbolas don't have an eccentricity, only ellipses have one.