SOLUTION: Write the equation of the hyperbola. Co - Ve Vertices: (1, 5) , (1, 1) Focus : (4, 3)

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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