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The hyperbola \(\frac{(x-3)^2}{5^2} - \frac{(y-17)^2}{12^2} = 1\) has two foci, which have different coordinates. Find the coordinates of the one with the larger x-coordinate.

 Nov 27, 2018
 #1
avatar+107480 
+3

You can get your knowledge and consequently your answer from here.

 

https://www.youtube.com/watch?v=zataIe8dvgY

 

Here is the graph if you want to play with it

 

https://www.desmos.com/calculator/ikcielfsgv

 

And here is the pic ofthe graph

 

 Nov 27, 2018
 #2
avatar+107348 
+1

Thanks, Melody

 

Here's an algebraic solution

 

We have  the form

 

(x - h)^2           (y - k)^2

_______    -    ________     =   1

   a^2                  b^2

 

The center    is (h, k)       =   ( 3, 17)

 

Since "x" comes first in this form.....the foci will lie on the horizontal axis

 

The focal point with the larger x coordinate is given by

 

(  3  + √ [ a^2 + b^2 ] , 17 )     = ( 3 + √ [5^2 + 12^2], 17 ) =  ( 3 + 13, 17) =

 

(16, 17 )

 

 

cool cool cool

 Nov 27, 2018
 #3
avatar+107480 
0

I already showed ant1 where to find the algebraic solution.

Why do you want to do all the thinking for everyone Chris?

Melody  Nov 27, 2018

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