SOLUTION: Find the equation of the hyperbola for each given condition. c. Center at (-2, 2); a focus at (6, 2); and a vertex at (4,2)

Algebra ->  Finance -> SOLUTION: Find the equation of the hyperbola for each given condition. c. Center at (-2, 2); a focus at (6, 2); and a vertex at (4,2)      Log On


   

Question 1191119: Find the equation of the hyperbola for each given condition.
c. Center at (-2, 2); a focus at (6, 2); and a vertex at (4,2)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1
given:
Center at (-2,2)=>h=-2, k=2
a focus at (6,2)=> focus is (h+-+c, k+) = (6,2)=>-2+-+c=6=>-2-6=c=>c=-8
a vertex at (4,2).=> (h+%2B+a, k) = (4, 2)=>-2+%2B+a=4=>a=2%2B4=>a=6
b%5E2=c%5E2-a%5E2
b%5E2=%28-8%29%5E2-6%5E2
b%5E2=64-36
b%5E2=28
equation is:
%28x-%28-2%29%29%5E2%2F6%5E2-%28y-2%29%5E2%2F28=1
%28x%2B2%29%5E2%2F36-%28y-2%29%5E2%2F28=1