Conic sections - HyperbolaIf we are given a 2 degree curve equation of a hyperbola, is there a way to find the centre, foci, eccentricity and directrices of a hyperbola , just as we can obtain the equation using foci, eccentricity, and directrix? I searched for it, but only found an answer for ellipse.

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luthersavage6lm · Accepted Answer

Step 1It is nearly the same equations as you would use for an ellipse.If you can get it into this form             (      x      −      h              )        2                    a      2        −            (      y      −      v              )        2                    b      2        =  1thencenter: (h,v)vertices are at   (  h  ±  a  ,  v  )  c  =            a      2        +          b      2      The eccentricity is   e  =      c    a  .The foci are at   (  h  ±  c  ,  v  ) the directrix is at   x  =  h  ±            a      2        c  if   −            (      x      −      h              )        2                    a      2        +            (      y      −      v              )        2                    b      2        =  1Step 2Then some of the equations above will swap a for b and the changes will be happening on a vertical, instead of a horizontal axis.Comparison to an ellipse             (      x      −      h              )        2                    a      2        +            (      y      −      v              )        2                    b      2        =  1 if   a  &amp;gt;  bcenter: (h, v)vertices:   (  h  ±  a  ,  v  )  c  =            a      2        −          b      2      eccentricity:   e  =      c    a  foci:   (  h  ±  c  ,  v  )directrix:   x  =  h  ±            a      2        c

If we are given a 2 degree curve equation of a hyperbola, is there a way to find the centre, foci, eccentricity and directrices of a hyperbola, just as we can obtain the equation using foci, eccentricity, and directrix?

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