SOLUTION: I am taking an online class and it did not come with a book! If someone could at least show me how to work it out, that would be much appreciated! Find the center, vertices, and

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I am taking an online class and it did not come with a book! If someone could at least show me how to work it out, that would be much appreciated! Find the center, vertices, and      Log On


   

Question 849052: I am taking an online class and it did not come with a book! If someone could at least show me how to work it out, that would be much appreciated!
Find the center, vertices, and foci of the hyperbola given by the equation (y-6)^2/4 - (x-4)^2/5 = 1.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

%28y-k%29%5E2%2Fb%5E2+-+%28x-h%29%5E2%2Fa%5E2+=+1



 %28y-6%29%5E2%2F2%5E2+-+%28x-4%29%5E2%2F5+=+1+

C(4,6)  Note: x = 4, 

V(4,8) and V(4,4)

Foci: sqrt%28a%5E2%2Bb%5E2%29 = sqrt%2810%29 Foci are: (4, 6+sqrt(10), (4, 6-sqrt(10))



Standard Form of an Equation of an Hyperbola opening up and down is:

  %28y-k%29%5E2%2Fb%5E2+-+%28x-h%29%5E2%2Fa%5E2+=+1 with C(h,k) and vertices 'b' units up and down from center,  2b the length of the transverse axis

Foci sqrt%28a%5E2%2Bb%5E2%29units units up and down from center, along x = h

& Asymptotes Lines passing thru C(h,k), with slopes m =  ± b/a



Standard Form of an Equation of an Hyperbola opening right and  left is:

  %28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 with C(h,k) and vertices 'a' units right and left of center,   2a the length of the transverse axis

Foci are sqrt%28a%5E2%2Bb%5E2%29 units right and left of center along y = k

& Asymptotes Lines passing thru C(h,k), with slopes  m =  ± b/a