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

 

Option: 1

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


Option: 2

\mathrm{xy=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

Here, focus \mathrm{(S) = (1, -1),} eccentricity \mathrm{(e) = \sqrt{2}}
From definition , \mathrm{SP=e\ PM}
\mathrm{\sqrt{(x-1)^2+(y+1)^2}=\frac{\sqrt{2} \cdot(x-y+1)}{\sqrt{1^2+1^2}}}
\mathrm{\Rightarrow(x-1)^2+(y+1)^2=(x-y+1)^2 \Rightarrow 2 x y-4 x+4 y+1=0}, which is the required equation of conic (Rectangular hyperbola)

 

 

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manish painkra

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