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The locus of the mid-points of the porti...

The locus of the mid-points of the portion of the tangents to the ellipse `(x^2)/(a^2) + (y^2)/(b^2) = 1` intercepted between the axes is

A

`(x^2)/(a^2) + (y^2)/(b^2) = 4`

B

`(a^2)/(x^2) + (b^2)/(y^2) = 4`

C

`(x^2)/(a^2) - (y^2)/(b^2) = 4`

D

none of these

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The correct Answer is:
B
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ML KHANNA-THE ELLIPSE-PROBLEM SET (2) (Multiple Choice Questions)
  1. The area of rectangle formed by perpendiculars from the centre of elli...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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