1. Graph the ellipse. (x-2)^2/9 + (y+1)^2/36 =1 Name the coordinates of the center, endpoints of major axis, endpoints of minor axis, and foci of the ellipse.
endpoint of major axis: and
endpoint of minor axis: and
2. LORAN is a long range hyperbolic navigation system. Suppose two LORAN transmitters are located at the coordinates (−100,0) and (100, 0) , where unit distance on the coordinate plane is measured in miles A receiver is located somewhere in the first quadrant. The receiver computes that the difference in the distances from the receiver to these transmitters is 180 miles. What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola?
The equation of the hyperbola that the receiver sits on is:
Center ( 2, -1)
Endpoints of major axis = (2, 5) and ( 2, -7)
Endpoints of minor axis = ( -1,-1) and ( 5, -1)
c = √ (a^2 - b^2) = √[36 - 9 ] = √27 = 3√3
So foci are at ( 2, -1 + c) and ( 2, -1 - c) = (2, -1 + 3√3) and ( 2 , -1 - 3√3)
Here's the graph : https://www.desmos.com/calculator/zpnpym9mx0