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The locus of the foot of the perpendicul...

The locus of the foot of the perpendicular drawn from the centre of the ellipse `(x^(2))/( a^(2)) +(y^(2))/( b^(2)) =1` to any of its tangents is

A

` (x^(2) -y^(2)) ^(2) =a^(2) x^(2) + b^(2) y^(2) `

B

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

C

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

D

` (x^(2) + y^(2) )^(2) =a^(2) x^(2) -b^(2) y^(2)`

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-REVISION EXERCISE -ELLIPSE
  1. The locus of the mid points of the normal chords of ( x^(2) ) /(a^(2))...

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  2. Tangents are drawn through the point (4, sqrt3) to the ellipse (x^(2...

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  3. The locus of the foot of the perpendicular drawn from the centre of th...

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  4. The locus of the mid points of parallel chords of an ellipse is a strr...

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  5. If the locus of the mid points of the chords of the ellipse (x^(2))/(a...

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  6. A point moves such that the distance from the point (2,0) is always 1...

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  7. Tangents are drawn to the ellipse (x^(2))/(a^(2)) +(y^(2))/( b^(2)) =a...

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  8. The nature of inter cepts made on the axes by the tangent at the point...

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  9. If the ellipse (x^(2))/( 4) + y^(2) =1 meets the ellipse x^(2) +(y^(...

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  10. Angle substended by common tangents of two ellipse 4( x-4) ^(2) +25y^(...

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  11. The line x= t^(2) meet the ellipse x^(2) +(y^(2))/( 9) =1 in the rea...

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  12. If S and S' are the foci of the ellipse (x^(2))/( 25)+ ( y^(2))/( 16) ...

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  13. If a tangent of slope 2 of the ellipse (x^(2))/( a^(2)) +(y^(2))/( b^...

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  14. Statement 1: In a triangle ABC , If base BC is fixed and perimeter of ...

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  15. An ellipse drawn by taking a diameter of the circle (x-1)^(2)+y^(2)=1 ...

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  16. Statement 1: In an ellipse the sum of the distances between foci is al...

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  17. Statement 1: Any chord of the conic x^(2) +y^(2) +xy = 1 through (0,0...

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  18. Statement 1: The area of the ellipse 2x^(2) +3y^(2) =6 is more than t...

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  19. Statement 1: An equation of a common tangent to the parabola y^(2) =16...

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  20. The equation of the circle passing through the foci of the ellipse (x^...

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