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.

ant101
Nov 27, 2018

#1**+2 **

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

Melody
Nov 27, 2018

#2**+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 )

CPhill
Nov 27, 2018