SOLUTION: Identify the center, vertices, and foci of this hyperbola: ((x-1)^2 / 4) - ((y-3)^2 / 9) = 1

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Question 879416: Identify the center, vertices, and foci of this hyperbola:
((x-1)^2 / 4) - ((y-3)^2 / 9) = 1
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

%28x-1%29%5E2+%2F2%5E2+-+%28y-3%29%5E2+%2F+9+=+1+ opening right and left along y = 3

C(1,3)

V(3,3) and V(-1,3)  ( 1+2  and 1-2)

c= sqrt(4+9) = sqrt(13)

Foci: f(1+√13, 3) and f(1-√13, 3)



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