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If the normal at one end of the latus re...

If the normal at one end of the latus rectum of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` passes through one end of the monor axis, then prove that eccentricity is constant.

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The equation of the normal at the extermity P of latus reactum is `x-ey=ae^(3)`
This passes through the extermity of the minor i.e.,B'(0,-b).
Then, `0+eb-ae^(3)=0`
`or ba^(2)" " or b^(2)=a^(2)e^(4)`
or `a^(2)(1-e^(2))=a^(2)e^(4)" " or e^(4)+e^(2)-1=0`
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