Question

Slete the following: Find the intercepts and domain and perform the symmetry test on each of the following hyperbolas. (a) 9x2 - 16y2 = 144 (g) -9x2 + 16y2 = 144 Graph the vertices, foci, endpoints of the conjugate axis, fundamental rectangle, and asymptotes, then draw the hyperbola for each equation in problem 1. = (6) 9x² - y² = 9 (d) 2532 - 36 = 900 (1) -25x + 4y = 100 (h) x² + 4y² = 16 of the martial hyperbola with equation finib ? - al. Find the length of AB using (c) 25x2 – 4y2 = 100 (e) –x2 + y2 = 1

Answer 1

Hyperbolas

-x^2 + 4y^2 = 16

Divide by 4 , write

-x^2/4 + y^2 = 16/4= 4

Now graph function

Vertices ( 4,0) and (-4,0)

Foci = (4.5, 0) and (-4.5,0)

(Demonstration Foci= √4^2 + 2^2 = √20 = 4.5)

Asymtptotes y = -2/4X and y= 2/4X

Endpoint of conjugates are (0,2) and (0,-2). (also named covertex)