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1. (5 pts.) For the hyperbola with equation 25y2 - 36x2 = 900 Determine the center, principal axis, and the vertices. Also sketch the hyperbola. 2. (5 pts.) Find an equation of the hyperbola whose foci are the vertices of the ellipse 7x2 + 11y2 = 77 and whose vertices are the foci of this ellipse. 3. (5 pts.) The vertices of a hyperbola are (-3, -1) and (-1,1) and the distance between the foci is 2v5. Find the equation of its asymptotes. 4. (5 pts.) Graph the equation xy + 16 = 0 by removing the xy term and show both sets of axes. 5. (5 pts.) Two LORAN stations A and B lie on a line running east and west, and A is 80 miles due east of B. An airplane is traveling east on a straight-line course that is 60 miles north of the line through A and B. Signals are sent at the same time from A and B, and the signal from A reaches the plane 350 usec before the one from B. If the signal travel at a rate of 0.2 mi//sec, locate the position of the plane by definition of a hyperbola