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How to find focus,vertex,directrix of a parabola like $x^2+y^2+2xy-6x-2y+3=0$. Well i know how to find those for any parabola of form $y^2=4ax$ but im just not being able to figure out a way to convert the given equation to this form. Help Please.

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  • $\begingroup$ Rotate the parabola, compute the focus, vertex, and directrix of the new figure, then apply the inverse rotation to them. $\endgroup$ – Lucian Mar 18 '15 at 20:21
  • $\begingroup$ just a few more links explaining rotation of axes here and here and here $\endgroup$ – Mirko Mar 18 '15 at 21:00
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    $\begingroup$ Hey thank you both!i just now figured it out!!Thanks a ton!!The focus is (1,1),directrix as y=x+1 and vertex (3/4,5/4). $\endgroup$ – user220382 Mar 18 '15 at 21:13

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