Home » Blog » Prove that the points on each branch of a hyperbola satisfy a property Prove that the points on each branch of a hyperbola satisfy a property by RoRi May 31, 2016 Prove that on each branch of a hyperbola the difference is a constant. Proof. Incomplete. Related
July 1, 2023 at 7:35 am S says: let X=(x,y) and N=(1,0). Then XN=x and |ex|<=|a|. Since a0, the difference is -2a. If ex<0, the difference is 2a.
![\[ \lVert X - F \rVert - \lVert X + F \rVert \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-a66ee519c99213b4df42cf5ce8abb441_l3.png "Rendered by QuickLaTeX.com")
let X=(x,y) and N=(1,0). Then XN=x and |ex|<=|a|. Since a0, the difference is -2a. If ex<0, the difference is 2a.