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 dist

Question 1180953: 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) (Show Source): You can put this solution on YOUR website!
You have the distance between the foci is
->
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:
->
Another property is that

from which you can find (half the conjugate axis), .
Since the foci are on a horizontal line, your hyperbola is oriented .
The halfway between the foci, in this case at the .
So the equation is

with in this case.

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