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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.

A

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

B

`e^2 - e + 1 = 0`

C

`e^2 + e + 1 = 0`

D

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

Text Solution

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The correct Answer is:
D
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ML KHANNA-THE ELLIPSE-PROBLEM SET (2) (Multiple Choice Questions)
  1. An ellipse slides between two perpendicular lines the locus of ...

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  2. The line 2x+y=3 cuts the ellipse 4x^(2)+y^(2)=5 at points P and Q. If ...

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  3. If the normal at one end of the latus rectum of the ellipse (x^2)/(...

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  4. Find the equation of the normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)...

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  5. The area of rectangle formed by perpendiculars from the centre of elli...

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  6. If the normal at the point P( theta) to the ellipse (x^(2))/(14)...

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  7. The locus of the mid-points of the portion of the tangents to the elli...

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  8. Tangents are drawn to x^2 + 3y^2 = 2. The locus" of mid-point of inter...

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  9. Tangents are drawn to ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1 at points ...

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  10. The locus of the point of intersection of tangents to an ellipse at tw...

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  11. The eccentric angles of extremities of a chord of an ellipse (x^2)/(a^...

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  12. The tangent at a point P(acosvarphi,bsinvarphi) of the ellipse (x^2)/(...

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  13. If the line x+2y+4=0 cutting the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2...

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  14. If P Q R is an equilateral triangle inscribed in the auxiliary circle ...

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  15. On the ellipse 4x^(2)+9y^(2)=1, the points at which the tangent are pa...

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  16. Tangents are drawn to the ellipse 3x^2 + 5y^2 = 32 and 25x^2 +9y^2 = 4...

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  17. Let two perpendicular chords of the ellipse (x^2)/(a^2) + (y^2)/(b^2) ...

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  18. An ellipse passes through the point (4,-1) and touches the line x+4...

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

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  20. The normal at a variable point P on the ellipse (x^2)/(a^2)+(y^2)/(b^2...

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