Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (1, O), (5, 0); fed: (0, 0), (6, 0) E Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE.) x2 = 1 36 4 center ( x, y ) = vertices ( x, y ) = (smaller x-value) ( x, y ) = (larger x-value) foci ( x, y ) = (smaller x-value) ( x, y ) = (larger x-value) asymptotes ( negative slope) (positive slope)Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE.) ( x - 1)2 _ (y + 3)2 = 1 9 1 center ( x, y ) = vertices ( x, y ) = (smaller x-value) ( x, y ) = (larger x-value) foci ( x, y ) = (smaller x-value) ( x, y ) = (larger x-value) asymptotes (negative slope) (positive slope)Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE.) 4x2 - y2 - 24x - 10y + 7 = 0 center ( x, y ) = vertices ( x, y ) = (smaller x-value) ( x, y ) = (larger x-value) foci ( x, y ) = (smaller x-value) ( x, y ) = (larger x-value) asymptotes (negative slope) (positive slope)Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. (If an answer does not exist, enter DNE.) x2 - 9y2 + 90y - 261 = 0 center ( x, y ) = vertices ( x, y ) = (smaller x-value) ( x, y ) = (larger x-value) foci ( x, y ) = (smaller x-value) ( x, y ) = (larger x-value) asymptotes (negative slope) (positive slope)Long-distance radio navigation for aircraft and ships uses synchronized pulses transmitted by widely separated transmitting stations. These pulses travel at the speed of light (186,000 miles per second). The difference in the times of arrival of these pulses at an aircraft or ship is constant on a hyperbola having the transmitting stations as foci. Assume that two stations 300 miles apart are positioned on a rectangular coordinate system with coordinates (150, 0) and (150, 0), and that a ship is traveling on a hyperbolic path with coordinates (X, 74) (see gure). y (a) Find the x-coordinate of the position of the ship when the time difference between the pulses from the transmitting stations is 1000 microseconds (0.001 second). (Round your answer to one decimal place.) mi (b) Determine the distance between the port and station A. (Round your answer to one decimal place.) mi (c) Find a linear equation that approximates the ship's path as it travels far away from the shore
