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Point | Distance to F1(2.646,0) | Distance to F2(-2.646,0) | Sum of Distances | Difference of Distances |
---|---|---|---|---|
P(3,1.936) | 1.969 | 5.969 | ∣1.969+5.9689∣=7.938 | ∣1.969−5.969∣=4 |
Q(-3.3,-2.273) | 6.365 | 2.365 | ∣6.365+2.365∣=8.73 | ∣6.365−2.365∣=4 |
R(2.5,-1.299) | 1.307 | 5.307 | ∣1.307+5.307∣=6.614 | ∣1.307−5.307∣=4 |
From the table above we see that the sum of the distances is not constant, which means that the given statement is false. However, we notice that the absolute value of the difference of the distances is constant.
A hyperbola is the set of all points in a plane such that the absolute value of the difference of the distances from any point on the hyperbola to two given points is constant. |