SOLUTION: Find the equation in standard form of the hyperbola whose foci are F1(−4√2,0) and F2(4√2,0), such that for any point on it, the absolute value of the difference of its distan

Algebra ->  Finance -> SOLUTION: Find the equation in standard form of the hyperbola whose foci are F1(−4√2,0) and F2(4√2,0), such that for any point on it, the absolute value of the difference of its distan      Log On


   

Question 1180958: Find the equation in standard form of the hyperbola whose foci are F1(−4√2,0) and F2(4√2,0), such that for any point on it, the absolute value of the difference of its distances from the foci is 8.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

You have the distance between the foci is
8sqrt%282%29+=+2c -> c+=4sqrt%282%29
A property of hyperbolas is that the absolute value of the difference of the distances from the foci is equal to the length of the transverse axis:
8+=+2a -> a+=+4
Another property is that
a%5E2+%2B+b%5E2+=+c%5E2+
from which you can find b (half the conjugate axis), b+=+4.
Since the foci are on a horizontal line, your hyperbola is oriented horizontally.
The center halfway between the foci, in this case at the origin.
So the equation is
x%5E2%2Fa%5E2+-+y%5E2%2Fb%5E2+=+1+
with a+=+b+=+4 in this case.
x%5E2%2F4%5E2+-+y%5E2%2F4%5E2+=+1+
x%5E2%2F16+-+y%5E2%2F16+=+1+