Practice!

Sample Problem

Find the foci of the hyperbola 9y2-x2-36y-6x-18=0

Solution

9y2-x2-36y-6x-18=0

9y2-36y-x2-6x=18

9(y2-4y)-(x2+6x)=18

9(y2-4y+4)-(x2+6x+9)= 18+36-9

9(y-2)2-(x+3)2=45

Since the y2 term is positive, we know the transverse axis is vertical and a2=5 and b2=45.

From c2=a2+b2=45+5=50

The center of this hyperbola is at (-3, 2) and the foci are therefore at (-3, 2+√50) and (-3, 2-√50)=

(-3, 2+5√2) and (-3, 2-5√2)