SOLUTION: Find the equation of hyperbola, foci at (3,5) and (3,-5), length of transverse axis is 6.

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Question 1186713: Find the equation of hyperbola, foci at (3,5) and (3,-5), length of transverse axis is 6.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of hyperbola,
given:
foci at (3,5) and (3%2C%7B%7B%7B-5),
the center is half way between, C(3,0)=> h=3 and k=0
length of transverse axis is 6=>2a=6=>a=3
Standard form of equation for a hyperbola with a vertical transverse axis :
%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1+
The distance between the foci is 2c.
in your case 2c=10->c=5
then
c%5E2+=+a%5E2+%2B+b%5E2
5%5E2+=+3%5E2+%2B+b%5E2
25+-+9+=+b%5E2
16=+b%5E2
b=4
substitute all known values in
%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1+
%28y-0%29%5E2%2F3%5E2-%28x-3%29%5E2%2F4%5E2=1+
y%5E2%2F9-%28x-3%29%5E2%2F16=1+ -> your equation