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If the normals at an end of a latus rect...

If the normals at an end of a latus rectum of an ellipse passes through the other end of the minor axis, then prove that `e^(4) + e^(2) =1.`

A

`e^(4)+e^(2)-1=0`

B

`e^(2)+e-5=0`

C

`e^(3) =sqrt(5)`

D

none of these

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FIITJEE-ELLIPSE-ASSIGNMENT PROBLEMS (OBJECTIVE) (LEVEL-I)
  1. Let P be a variable point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 wit...

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  2. If the chords of contact of tangents from two poinst (x1, y1) and (...

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  3. If the normals at an end of a latus rectum of an ellipse passes throug...

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  4. An ellipse having coordinate axes as its axes and semi major and semi ...

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  5. Let E be the ellipse (x^(2))/(9)+(y^(2))/(4)=1 and C be the circle x^(...

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  6. A tangent is drawn to the ellipse (x^(2))/(27)+y^(2)=1 at the point (3...

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  7. The area of the quadrilateral formed by the tangents at the endpoint o...

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  8. P is any point on the ellipise (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and S...

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  9. The curve with parametric equations x=1+4 cos theta, y=2+3 sin theta ...

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  10. Find the eccentricity of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 whose la...

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  11. A perfectely rough plane is inclined at an angle alpha to the horizont...

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  12. The locus of the point of intersection of the tangents drawn to the el...

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  13. An ellipse of major and minor axes of length sqrt(3) and 1 respectivel...

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  14. A tangent to the ellipse 4x^2 +9y^2 =36 is cut by the tangent at the e...

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  15. Angle between tangents drawn from any point on the circle x^2 +y^2 = (...

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  16. The locus of point intersection of perpendicular tangents of ellipse (...

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  17. If alpha, beta are the eccentric angles of the extermities of a focal ...

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  18. Locus of mid-point of the focal chord of ellipse (x^(2))/(a^(2))+(y^(...

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  19. The locus of foot of perpendicular from focus of ellipse (x^(2))/(a^(2...

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  20. The length of common chord of ellipse ((x-10)^(2))/(100)+((y-21)^(2))/...

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