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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.

 

Answer:

 

center:

 

endpoint of major axis:      and

 

endpoint of minor axis:      and

 

foci:        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?

Answer:

a=

b=

c=

The equation of the hyperbola that the receiver sits on is: 

 Nov 13, 2019
 #1
avatar+105411 
+1

First one

 

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

 

 

cool cool cool

 Nov 13, 2019
 #2
avatar+105411 
+1

For the second, see here :    https://web2.0calc.com/questions/loran-question 

 

 

a  = √8100  = 90

b =  √1900  = 10√19

c = √10000  = 100 

 

 

cool cool cool

 Nov 13, 2019

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