SOLUTION: Find the equation of the hyperbola for each given conditions. b. Center at (2,2), a focus at (10,2) and a vertex at (5,2).

Algebra ->  Finance -> SOLUTION: Find the equation of the hyperbola for each given conditions. b. Center at (2,2), a focus at (10,2) and a vertex at (5,2).      Log On


   

Question 1191090: Find the equation of the hyperbola for each given conditions.
b. Center at (2,2), a focus at (10,2) and a vertex at (5,2).
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 (10,2)=> focus is (h+-+c, k+) = (10,2)=>2+-+c=10=>2-10=c=>c=-8
a vertex at (5,2).=> (h+%2B+a, k) = (5, 2)=>2+%2B+a=5=>a=2-5=>a=-3
b%5E2=c%5E2-a%5E2
b%5E2=%28-8%29%5E2-%28-3%29%5E2
b%5E2=64-9
b%5E2=55
equation is:
%28x-2%29%5E2%2F9-%28y-2%29%5E2%2F55=1