SOLUTION: Find the center, vertices, and foci of the hyperbola given by the equation (y-1)^2/9 - (x-2)^2/16 = 1 Please include steps on how to solve so I can understand.

Algebra ->  Trigonometry-basics -> SOLUTION: Find the center, vertices, and foci of the hyperbola given by the equation (y-1)^2/9 - (x-2)^2/16 = 1 Please include steps on how to solve so I can understand.       Log On


   

Question 860404: Find the center, vertices, and foci of the hyperbola given by the equation
(y-1)^2/9 - (x-2)^2/16 = 1 Please include steps on how to solve so I can understand.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

%28y-1%29%5E2%2Fhighlight_green%283%5E2%29+-+%28x-2%29%5E2%2F16+=+1 C(2,1) opening Up and down along x = 2

Vertices: V(2,-2) and V(2,4) highlight_green%283%29 units up and down from center

foci: F(2,-4) and F(2, 6)  |sqrt%289%2B16%29| = 5 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