Question

29) Find the equation of the ellipse whose eccentricity is
the focus is (-1,1) and the directrixis is x_y+3=0
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Answer 1

7x2+2xy+7y2+10x−10y+7=07x2+2xy+7y2+10x−10y+7=0

Given focus is (1,−1)(1,−1) and equation of the directrix is x−y=3x−y=3

Eccentricity e=12e=12

Hence SP=ePMSP=ePM

SP2=e2PM2SP2=e2PM2

(ie) SP2=14SP2=14(PM)2(PM)2

4SP2=PM24SP2=PM2

(ie) 4[(x+1)2+(y−1)2]=(x−y−312+(−1)2−−−−−−−−√)24[(x+1)2+(y−1)2]=(x−y−312+(−1)2)2

⇒8(x2+y2+2x−2y+2)=(x−y+3)2




hope it's helpful