SOLUTION: Identify the center, vertices, foci, transverse, asymptotes, domain, and range for the following hyperbola: ((y-2)^2 / 9) - ((x^2) / 36) = 1

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Identify the center, vertices, foci, transverse, asymptotes, domain, and range for the following hyperbola: ((y-2)^2 / 9) - ((x^2) / 36) = 1       Log On


   

Question 879417: Identify the center, vertices, foci, transverse, asymptotes, domain, and range for the following hyperbola:
((y-2)^2 / 9) - ((x^2) / 36) = 1
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

%28y-2%29%5E2+%2F3%5E2+-+x%5E2%2F+36+=+1 opening Up and down along x = 0

C(0,2)

V(0,5) and V(0,-1)  |  2+3, 2-3

c= sqrt(9+36) = sqrt(45)

Foci: f(0, 3+√45) and f(0, 3-√45)



Need to Know...............................................................

Standard Form of an Equation of a Circle is %28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2 

Standard Form of an Equation of an Ellipse is %28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1+ 

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 

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 

the vertex form of a Parabola opening up(a>0) or down(a<0), y=a%28x-h%29%5E2+%2Bk

 the vertex form of a Parabola opening right(a>0) or left(a<0), x=a%28y-k%29%5E2+%2Bh