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let P be a point the first quadrant lyin...

let P be a point the first quadrant lying on the ellipse `9x^(2) +16y^(2) =144, ` such that the tangent at P to the ellipse is
inclined at an angle ` 135^(@) ` to the positive direction of x-axis Then the coordinates of P are

A

` ((sqrt(143))/( 3), (1)/(4) ) `

B

` ( ( 8)/(9) , (sqrt(77))/( 3))`

C

` ((4)/(sqrt2), ( 3)/(sqrt2))`

D

` ((16)/(5), ( 9)/(5))`

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-REVISION EXERCISE -ELLIPSE
  1. The line x= t^(2) meet the ellipse x^(2) +(y^(2))/( 9) =1 in the rea...

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

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

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

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

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

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

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

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

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

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  11. The locus of the foot of perpandicular drawn from the centre of the e...

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  12. If and c are positive real number and the ellipse (x^(2))/( 4c^(2)) +...

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  13. Let the equation of two ellipse be E1:( x^(2))/( 3)+ ( y^(2))/( 2) =1 ...

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  14. If the curves (x^(2))/(alpha)+(y^(2))/(4)=1 and y^(3)=16x intresect a...

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  15. A point on the ellipse 4x^(2) +9y^(2) = 36 where the normal is paralle...

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  16. If OB is the semi-minor axis of an ellipse , F1 and F2 are its foci an...

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  17. The minimum area of a triangle formed by any tangent to the ellipse (x...

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  18. The tangent to the ellipse 3x^(2) +16y^(2) =12,at the point (1,3//4) ...

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  19. let P be a point the first quadrant lying on the ellipse 9x^(2) +16y^(...

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  20. The area (in sq . Unit ) of the quadrilateral formed by the tangents a...

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