I was studying about the properties (foci , directrix and axis) of the conics. There all the properties were given for only the conic with axis along the co-ordinate axes . Then a question suddenly hit my mind - How can we find the properties of a conic given in general form (ax²+2hxy+by²+2gx+2fy+c=0) ? Please anybody help me.
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See this answer for foci and directrix. The axes are $h^3y^2-abhy^2-bh^2xy+ah^2xy+ab^2xy-a^2bxy+2gh^2y-bfhy-afhy+b^2gy-abgy-h^3x^2+abhx^2-2fh^2x+bghx+aghx+abfx-a^2fx+g^2h-f^2h+bfg-afg=0.$ – Jan-Magnus Økland May 10 '20 at 06:03
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1I am a student of only 12th . Therefore I couldn't make out what is answered and how . Can you please tell me what is the conclusion and the law to find them out. – zombie May 10 '20 at 06:43