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The normal at a variable point `P` on the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` of eccentricity `e` meets the axes of the ellipse at `Qa n dRdot` Then the locus of the midpoint of `Q R` is a conic with eccentricity `e '` such that `e^(prime)` is independent of `e` (b) `e^(prime)=1` `e^(prime)=e` (d) `e^(prime)=1/e`

A

`e = 1`

B

`e = 1//e`

C

`e' = e`

D

none

Text Solution

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The correct Answer is:
C
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ML KHANNA-THE ELLIPSE-PROBLEM SET (2) (Multiple Choice Questions)
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  3. The locus of the point of intersection of tangents to an ellipse at tw...

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

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

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

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

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

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

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

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

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

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

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  14. If P(theta1) and D(theta2) be the end, points of two semi-conjugate di...

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  15. If CP and CD are semi-conjugate diameters of the ellipse x^(2)/a^(2) +...

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  16. CP and CD are conjugate semi-diameters of the ellipse x^(2)/a^(2) + y^...

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  17. The maximum distance of the centre of the ellipse (x^(2))/(16) +(y^(2)...

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  18. Tangents are drawn from the point P(3,4) to the ellipse x^(2)/9+y^(2)/...

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  19. Tangents are drawn from the point P(3, 4) to the ellipse x^2/9 +y^2/4 ...

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  20. Tangents are drawn from the point P(3,4) to the ellipse (x^2)/(9)+(y^2...

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