Which statement about the hyperbola is true?
The point (-3,0) is a focus.
The point (3, 0) is a vertex.
The transverse axis passes through the point (0,2).
The transverse axis has an endpoint at (5,0).
(5,0)
(-5,0)
6 5 4
2
1
1 2
1 4

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Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Evaluate the discriminant of each equation. tell how many solutions each equation has and whether the solutions are real or imaginary. 4x^2 + 20x + 25 = 0