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  • The equation of the conic with focus at , directrix along <img alt="\mathrm{x-y+1=0}" src="https://entrancecor

The equation of the conic with focus at (1,-1), directrix along \mathrm{x-y+1=0} and with eccentricity \sqrt{2} is

Option: 1

\mathrm{x^{2}-y^{2}=1}


Option: 2

\mathrm{x y=1}


Option: 3

\mathrm{2 x y-4 x+4 y+1=0}


Option: 4

\mathrm{2 x y+4 x-4 y-1=0}


Answers (1)

best_answer

Let \mathrm{P}(\mathrm{x}, \mathrm{y}) be any point on the conic. Then

\mathrm{\sqrt{(x-1)^{2}+(y+1)^{2}}=\sqrt{2}\left(\frac{x-y+1}{\sqrt{2}}\right)}   [Using SP= e.PM]

\mathrm{\Rightarrow 2 x y-4 x+4 y+1=0}

Posted by

sudhir.kumar

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