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The ellipse x^(2)+4 y^(2)=4 is inscribed...

The ellipse `x^(2)+4 y^(2)=4` is inscribed in a rectangle aligned with coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4,0) . Then the equation of the ellipse is

A

`4 x^(2)+64 y^(2)=48`

B

`x^(2)+16 y^(2)=16`

C

`x^(2)+12 y^(2)=16`

D

`4 x^(2)+48 y^(2)=48`

Text Solution

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The correct Answer is:
C
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HIMALAYA PUBLICATION-ELLIPSE-QUESTION BANK
  1. The line passing through the extremity A of the major axis and extremi...

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  2. A focus of an ellipse is at the origin. The directrix is the line x=4 ...

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  3. The ellipse x^(2)+4 y^(2)=4 is inscribed in a rectangle aligned with c...

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  4. Equation of the ellipse whose axes are the axes of co-ordinates and wh...

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  5. The foci of the ellipse 25(x+1)^(2)+9(y+2)^(2)=225 are at

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  6. The eccentricity of the ellipse 9 x^(2)+5 y^(2)-30 y=0 is

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  7. The eccentricity of an ellipse with centre at the origin which meets t...

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  8. The equation to the ellipse (referred to its axes as the axes of x and...

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  9. P is any point on the ellipse 9x^(2) + 36y^(2) = 324 whose foci are S ...

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  10. The line L x+m y+n=0 is a normal to the ellipse (x^(2))/(a^(2))+(y^(2)...

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  11. The angle between the pair of tangents drawn from the point (1,2) to t...

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  12. How many real tangents can be drawn to the ellipse 5 x^(2)+9 y^(2)=32 ...

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  13. If two tangents drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1...

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  14. The foci of the conic 25 x^(2)+16 y^(2)-150 x=175 are

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  15. The equation of the ellipse whose distance between the foci is equal t...

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  16. The eccentricity of the ellipse x^(2)+4 y^(2)+8 y-2 x+1=0 Is

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  17. The eccentricity of the conic 4 x^(2)+16 y^(2)-24 x-32 y=12 is

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  18. The radius of the circle passing through the foci of the ellipse (x^(2...

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  19. The equation of the ellipse having vertices at (pm5,0) and foci (pm4,0...

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  20. If theta is a parameter then x=a(sin theta+cos theta) y=b(sin theta-co...

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