SOLUTION: Write the equation of a hyperbola with foci at (3, -3) and (3, 7) and vertices at (3, -1) and (3, 5). Write the equation of a hyperbola with vertices (0, -4) and (0, 4) and fo

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the equation of a hyperbola with foci at (3, -3) and (3, 7) and vertices at (3, -1) and (3, 5). Write the equation of a hyperbola with vertices (0, -4) and (0, 4) and fo      Log On


   

Question 1081571: Write the equation of a hyperbola with foci at (3, -3) and (3, 7) and vertices at (3, -1) and (3, 5).

Write the equation of a hyperbola with vertices (0, -4) and (0, 4) and foci (0, -5) and (0, 5).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation of a hyperbola with foci at (3, -3) and (3, 7) and vertices at (3, -1) and (3,+5).
determine if it is
horizontal: %28x-h%29%5E2%2Fa%5E2+-%28y-k%29%5E2%2Fb%5E2+=1
or
vertical: %28y-k%29%5E2%2Fa%5E2+-+%28x-h%29%5E2%2Fb%5E2+=1
To start, let's graph the information we have:



so,you have vertical:
%28y-k%29%5E2%2Fa%5E2+-+%28x-h%29%5E2%2Fb%5E2+=1
now
1. Identify the center point (h, k)
it is midpoint of line segment:(3, -3) and (3, 7)
(%283%2B3%29%2F2, %28-3%2B7%29%2F2)=(3, 2)
The center point is (h, k)=(3, 2).
so,h=3 and k=2
put it on a graph:


2. Identify a and c
To find a, we'll count from the center to either vertex; a+=+3.
To find c, we'll count from the center to either focus;+c+=+5

3. Use the formula c%5E2+=+a%5E2+%2B+b%5E2 to find b (or b%5E2)
b%5E2=c%5E2+-a%5E2+
b%5E2=5%5E2+-3%5E2+
b%5E2=25+-9+
b%5E2=16+->b=4
4. Plug h=3, k=2, a=3, and b=4 into the correct pattern.
%28y-2%29%5E2%2F3%5E2+-+%28x-3%29%5E2%2F4%5E2+=1
%28y-2%29%5E2%2F9+-+%28x-3%29%5E2%2F16+=1




next problem is of same type; so,I am pretty sure you can do it following these steps