SOLUTION: I am so unsure of how to answer this question. not sure of any of the steps and need detailed explanation if possible Fidn the center, vertices,and foci of the hyperbola given

Algebra ->  Trigonometry-basics -> SOLUTION: I am so unsure of how to answer this question. not sure of any of the steps and need detailed explanation if possible Fidn the center, vertices,and foci of the hyperbola given       Log On


   

Question 860400: I am so unsure of how to answer this question. not sure of any of the steps and need detailed explanation if possible
Fidn 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-6%29%5E2%2Fhighlight_green%282%5E2%29+-+%28x-4%29%5E2%2F5=+1 C(4,6) opening Up and down along x = 4

Vertices: V(4,8) and V(4,4) highlight_green%282%29 units up and down from center

foci: F(4,9) and F(4,3)  | sqrt%284%2B5%29| = 3 units up and down from center

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