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When you are given the vertices and foci, it is possible to write the equation for the hyperbola.
\Because you can determine the values of ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=a299a8379d695518a923bda450d13381.png\")
, and ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=52257f1605fb2b790995dd69987af2c6.png\")
, and then use the relationship ![\"\"](\"/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=f3537f7183464a00f701c99bd6a33a0b.png\")
to find ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=b72515eceac9b0f2954ec68f910b8672.png\")
.
When you are given the vertices and the length of one of the axes or the slopes of the intercepts, you can find all of the values needed to write the equation.
\When you are given the foci and transverse axis you can find the values of , and ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=52257f1605fb2b790995dd69987af2c6.png\")
, and then use the relationship to find .
However, when you are given the vertices and transverse axis, it is not possible to write the equation for the hyperbola, because there is no way to determine the value of .