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Find the equation of ellipse having focu...

Find the equation of ellipse having focus at (1,2) corresponding directirx `x-y+2=0` and eccentricity `0.5`.

Text Solution

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The correct Answer is:
`7x^(2)+7y^(2)+2xy-20x-28y+36=0`
Equation of ellipse is locus of point (x,) such that SP= e. PM, where `S-=(1,2)` and M is foot of perpendicular from focus upon directirx.
Therfore, the equation of ellipse is
`sqrt((x-1)^(2)+(y-2)^(2))=(1)/(2)(|x-y+2|)/(sqrt(1^(2)+(-1)^(2)))`
or `8(x^(2)-2x+1-y^(2)-4y+4)=x^(2)+y^(2)+4+4x-4y-2xy`
or `7x^(2)+7y^(2)+2xy-20y+36=0`
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