SOLUTION: Hi there! Well I was wondering if I could please get some help finding the center and foci of this hyperbola. It would be good if I could see the work so I could understand the

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Hi there! Well I was wondering if I could please get some help finding the center and foci of this hyperbola. It would be good if I could see the work so I could understand the       Log On


   

Question 734009: Hi there!
Well I was wondering if I could please get some help finding the center and foci of this hyperbola. It would be good if I could see the work so I could understand the problem better. (y + 2) ^ 2 /4 - x ^ 2 / 12 = 1
thank you so much!
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
%28y+-+k%29+%5E+2+%2Fb%5E2++-+%28x-h%29+%5E+2+%2F+a%5E2+=+1 where h and k are the coordinates of the center

%28y+%2B+2%29%5E2+%2F4+-x%5E2+%2F12+=+1
k=-2, h=0,; so, the center is at (0,-2)
a%5E2=12...=> a=3.46 ....the semi-transverse axis is 3.46 unit
long
b%5E2=4...=> b=2...the semi-conjugate axis is 2 units
long
focus: c%5E2=a%5E2%2Bb%5E2
c%5E2=12%2B4
c%5E2=16
c=sqrt%2816%29
c=4 and c=-4.....The foci are c units right and left of the center:
(0,-2%2B4)=(highlight%280%29,highlight%282%29)
and (0,-2-4)=(highlight%280%29,highlight%28-6%29)