+0  
 
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avatar+315 

Trig

 May 7, 2019
 #1
avatar+106535 
+2

This hyperbola will have its center at (0,0)

Since  (√13, 0)  and (-√13,0) are the foci....the hyperbola will have the form   

 

x^2         y^2

___  -   ____  =   1

a^2         b^2

 

Since  the difference  in  distances from any point on the hyperbola to the focal points  = 6 , we have this property that

 

2a  =  6       divide both sides by  2

a =  3

a^2  = 9

 

And     a^2 + b^2  = c^2          where c = √13

 

So

 

3^2 + b^2  = (√13)^2

9 + b^2  = 13

b^2 = 13 - 9

b^2  = 4

 

So....the correct  form is

 

x^2        y^2

___  -    ___     =  1

 9            4

 

 

 

cool cool cool

 May 7, 2019
 #2
avatar+315 
+1

Thank you! smiley

Cupcake  May 7, 2019

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