SOLUTION: Find an equation in standard form for the hyperbola that satisfies the given conditions. Center at​ (0,0) a=4​, e=4​, horizontal focal axis

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Question 1134791: Find an equation in standard form for the hyperbola that satisfies the given conditions.
Center at​ (0,0) a=4​, e=4​, horizontal focal axis
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The standard form of a hyperbola that opens sideways is
%28x+-+h%29%5E2+%2F+a%5E2+-+%28y+-+k%29%5E2+%2F+b%5E2+=+1

if center at​ (0,0), means h=0 and k=0 and your equation is

x%5E2+%2F+a%5E2+-+y%5E2+%2F+b%5E2+=+1

if a=4%E2%80%8B,
x%5E2+%2F+4%5E2+-+y%5E2+%2F+b%5E2+=+1
if e=4%E2%80%8B, horizontal focal axis
e=c%2Fa
4=c%2F4
c=16
since c=sqrt%28a%5E2%2Bb%5E2%29...plug in a=4​, c=16 and solve for b
16=sqrt%2816%2Bb%5E2%29.......square both sides
16%5E2=%28sqrt%2816%2Bb%5E2%29%29%5E2
256=16%2Bb%5E2
b%5E2=256-16
b%5E2=240
b=4sqrt%2815%29

and your equation is
x%5E2+%2F+16+-+y%5E2+%2F+240+=+1