SOLUTION: 2. The equation of a hyperbola is given by (x-1)^2/16 - (y+1)^2/9 =1 a. Give the coordinates of the center of the hyperbola. b. Give the length of the transverse and conjugate a

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 2. The equation of a hyperbola is given by (x-1)^2/16 - (y+1)^2/9 =1 a. Give the coordinates of the center of the hyperbola. b. Give the length of the transverse and conjugate a      Log On


   

Question 616154: 2. The equation of a hyperbola is given by (x-1)^2/16 - (y+1)^2/9 =1
a. Give the coordinates of the center of the hyperbola.
b. Give the length of the transverse and conjugate axes.
c. Give the slopes of the asymptotes.
d. Give the coordinates of the foci.
e. Graph the hyperbola. Label the center, midpoints of the associated rectangle, and foci.
I have the first 2 done correctly I think. For a) 1, -1. For b) transverse 4, conjugate is 3.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi, 

%28x-1%29%5E2%2F16+-+%28y%2B1%29%5E2%2F9+=1 is %28x-1%29%5E2%2F4%5E2+-+%28y%2B1%29%5E2%2F3%5E2+=1

 a. Give the coordinates of the center of the hyperbola. Yes! C(1,-1)

 b. Give the length of the transverse axis highlight%282%29%2A4+=+8 and conjugate axes.2%2A3+=+6

 c. Give the slopes of the asymptotes. ±3/4 

-1 = 3/4(1)+b, b = -7/4, y = (3/4)x-7/4  OR y = (-3/4)x-1/4

 d. Give the coordinates of the foci.sqrt%2816%2B9%29=sqrt%2825%29+=+5 (1,4)&(1,-6)

 e. Graph the hyperbola. Label the center, midpoints of the associated rectangle, and foci.