Home
Class 12
MATHS
The ellipse x^2+""4y^2=""4 is inscribed ...

The ellipse `x^2+""4y^2=""4` is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is (1) `x^2+""16 y^2=""16` (2) `x^2+""12 y^2=""16` (3) `4x^2+""48 y^2=""48` (4) `4x^2+""64 y^2=""48`

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    AAKASH INSTITUTE|Exercise SECTION-C ( Objective Type Questions ( More than one answer))|1 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE|Exercise SECTION-C|45 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE|Exercise Assignment (SECTION - A)|55 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE|Exercise section-J (Aakash Challengers Qestions)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE|Exercise section - J|6 Videos

Similar Questions

Explore conceptually related problems

Ellipse x^(2) + 4y^(2) = 4 is inscribed in a rectangle aligned with co-ordinate axes . This rectangle itself is inscribed in another ellipse the passes ellipse that through (-4,0) . Then the equation of the ellipse is

An ellipse is drawn by taking a diameter of the circle (x""""1)^2+""y^2=""1 as its semiminor axis and a diameter of the circle x^2+""(y""""2)^2=""4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is (1) 4x^2+""y^2=""4 (2) x^2+""4y^2=""8 (3) 4x^2+""y^2=""8 (4) x^2+""4y^2=""16

The ellipse E_(1):(x^(2))/(9)+(y^(2))/(4)=1 is inscribed in a rectangle R whose sides are parallel to the coordinates axes. Another ellipse E_(2) passing through the point (0, 4) circumscribes the rectangle R. The length (in units) of the major axis of ellipse E_(2) is

The coordinates of a focus of the ellipse 4x^(2) + 9y^(2) =1 are

Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3,""1) and has eccentricity sqrt(2/5) is: (1) 3x^2+""5y^2-32""=""0 (2) 5x^2+""3y^2-48""=""0 (3) 3x^2+""5y^2-15""=""0 (4) 5x^2+""3y^2-32""=""0

For the ellipse 12x^(2)+4y+24x-16y+25=0

Find the equation of the largest circle with centre (1,0) that can be inscribed in the ellipse x^(2)+4y^(2)=16

Find the equation of the largest circle with centre (1,0) that can be inscribed in the ellipse x^(2)+4y^(2)=16

The distnce between the foci of the ellipse 3x ^(2) + 4y ^(2) =48 is

AAKASH INSTITUTE-CONIC SECTIONS-SECTION-B
  1. Number of points on the ellipse (x^(2))/(25) + (y^(2))/(16) =1 from wh...

    Text Solution

    |

  2. Area of the region bounded by the curve {(x,y) : (x^(2))/(a^(2)) + (y^...

    Text Solution

    |

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

    Text Solution

    |

  4. P is any variable point on the ellipse 4x^(2) + 9y^(2) = 36 and F(1), ...

    Text Solution

    |

  5. The curve described parametrically by x = t^2 + t +1, y = t^2 - t + 1 ...

    Text Solution

    |

  6. Find the equation of the common tangent to the curves y^2=8x and xy=-1...

    Text Solution

    |

  7. AB is double ordinate of the hyperbola x^2/a^2-y^2/b^2=1 such that Del...

    Text Solution

    |

  8. The equation of the hyperbola, whose foci are (6, 4) and (-4, 4) and e...

    Text Solution

    |

  9. The equation of the tangent to the hyperbola 3x^(2) - 4y^(2) = 12, whi...

    Text Solution

    |

  10. The equation (x^2)/(1-r)-(y^2)/(1+r)=1,r >1, represents an ellipse (b)...

    Text Solution

    |

  11. The equation of the hyperbola with centre at (0, 0) and co-ordinate ...

    Text Solution

    |

  12. The equation of the tangent to the hyperbola 3x^(2) - 8y^(2) = 24 and ...

    Text Solution

    |

  13. The locus a point P(alpha,beta) moving under the condition that the li...

    Text Solution

    |

  14. The locus of the middle points of the chords of hyperbola (x^(2))/(9) ...

    Text Solution

    |

  15. Let P(a sectheta, btantheta) and Q(aseccphi , btanphi) (where theta+...

    Text Solution

    |

  16. An ellipse has eccentricity 1/2 and one focus at the point P(1/2,1)....

    Text Solution

    |

  17. IF t is a parameter, then x = a(t + (1)/(t)) and y = b(t - (1)/(t)) re...

    Text Solution

    |

  18. If 3x^(2) - 5y^(2) - 6x + 20 y - 32 = 0 represents a hyperbola, then ...

    Text Solution

    |

  19. IF the locus of the point of intersection of two perpendicular tangent...

    Text Solution

    |

  20. If the line y = mx + sqrt(a^(2) m^(2) -b^(2)), m = (1)/(2) touches the...

    Text Solution

    |