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  4. If ends of latus rectum of parabola (x+1)2=4(y+1) are vertices of an ellipse whose eccentricity is half of eccentricity of parabola, then for ellipse,

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Q. If ends of latus rectum of parabola $(x+1)^2=4(y+1)$ are vertices of an ellipse whose eccentricity is half of eccentricity of parabola, then for ellipse,

Conic Sections

Solution:

image
Coordinate of foci $=(-1 \pm ae , 0)=(-2,0)$ and $(0,0)$
Equation of directrix $x=-1 \pm \frac{ a }{ e }$
$\Rightarrow( x +5)( x -3)=0$