+884 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.
+118608 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
+128408 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 )
