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puzzling mathworld formulas


at http://mathworld.wolfram.com/Ellipse.html , there are a set of equations called (22), (23). 
   
  which is the source used to verify, and is it possible to check their truth with mathematica? 
   
  but notice that no similar analagous formulas at http://mathworld.wolfram.com/Hyperbola.html . 
   
  are the ellipses formulas just lucky guesses or what? 
   
  does these also hold for ellipses that are called type imaginary ellipses?
   
  thanks!


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