Question 1187217: Write the equation of the hyperbola. Co - Ve Vertices: (1, 5) , (1, 1) Focus : (4, 3)
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! the equation of the hyperbola:
the length of the transverse axis is 
the coordinates of the vertices are ( ±  ,  )
the length of the conjugate axis is 
the coordinates of the co-vertices are ( , ± )
the distance between the foci is  , where 
the coordinates of the foci are ( ± , )
given:
Co -Vertices: ( ,  ) , (, )
we know that the center is half way between: ( , )=(, ) => so,  and 
use Co -Vertices: (, ), and to find 
( , ± )=(, )
( , ± )=(, )=>± =>±
the coordinates of the foci are ( ±, )= ( , ) =>( ±,)= (, ) => ± =>± =>±
then => =>
and your equation is:
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