A parabola is drawn with focus is at one of the foci of the ellipse (where ) and directrix passing through the other focus and perpendicular to the major axes of the ellipse. If latus rectum of the ellipse and the parabola are same, then the eccentricity of the ellipse is |
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a) |
b) |
c) |
d) |
None of these |

A parabola is drawn with focus is at one of the foci of the ellipse (where ) and directrix passing through the other focus and perpendicular to the major axes of the ellipse. If latus rectum of the ellipse and the parabola are same, then the eccentricity of the ellipse is |
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a) |
b) |
c) |
d) |
None of these |

1 Answer

127 votes

**(c)**

Equation of the ellipse is

Equation of the parabola with focus and directrix is

Now length of latus rectum of the ellipse is and that of the parabola is .

For the two latus recta to be equal, we get

Therefore,

Hence,

127 votes

127