Home
Class 11
MATHS
Show that : 4x^2+16y^2-24x-32y=12 is the...

Show that : `4x^2+16y^2-24x-32y=12` is the equation of ellipse, and find its vertices, foci, eccentricity and directrices.

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise EXERCISE|478 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

  • INFINITE SERIES

    MODERN PUBLICATION|Exercise EXAMPLE|10 Videos

Similar Questions

Explore conceptually related problems

Show that 4x^2+8x+y^2-4y+4=0 represents an ellipse. Find its eccentricity, co-ordinates of foci, equations of major and minor axes and latus-rectum.

Find the lengths of the major and minor axes, co-ordinates of the foci, vertices, the eccentricity and equations of the directrices for the ellipse 9x^2+ 16y^2 = 144 .

Show that the equation : 16x^2 -3y^2-32x -12y- 44 = 0 represents a hyperbola , and find the lengths of the axes and eccentricity.

Show that the equation (10x-5)^(2)+(10y-5)^(2)=(3x+4y-1)^(2) represents an ellipse, find the eccentricity of the ellipse.

If (5, 12) and (24, 7) are the foci of an ellipse passing through the origin, then find the eccentricity of the ellipse.

Find the equation of the ellipse whose focus is (1,-1), the corresponding directrix is x-y-3=0, and eccentricity is 1/2 .

Find the lengths of the major and minor axes, the co-ordinates of the foci, the vertices, the eccentricity, length of latus-rectum and equations of the directrices of the following ellipse : x^2+16 y^2 =16 .

Find the lengths of the major and minor axes, the co-ordinates of the foci, the vertices, the eccentricity, length of latus-rectum and equations of the directrices of the following ellipse : 16x^2+ y^2 =16 .

Find the lengths of the major and minor axes, the co-ordinates of the foci, the vertices, the eccentricity, length of latus-rectum and equations of the directrices of the following ellipse : x^2/36 +y^2/16=1 .

Find the lengths of the major and minor axes, the co-ordinates of the foci, the vertices, the eccentricity, length of latus-rectum and equations of the directrices of the following ellipse : x^2/16 +y^2/9 =1 .

MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. Find the equation of the ellipse whose foci are (2,3),(-2,3) and whose...

    Text Solution

    |

  2. Find the equation of the set of all points whose distances from (0, 4)...

    Text Solution

    |

  3. Show that : 4x^2+16y^2-24x-32y=12 is the equation of ellipse, and find...

    Text Solution

    |

  4. Show that 4x^2+8x+y^2-4y+4=0 represents an ellipse. Find its eccentric...

    Text Solution

    |

  5. Show that 4x^2+8x+y^2-4y+4=0 represents an ellipse. Find its eccentric...

    Text Solution

    |

  6. Find the centre, length of the axes, eccentricity and foci of the elli...

    Text Solution

    |

  7. In the ellipse 25x^(2)+9y^(2)-150x-90y+225=0

    Text Solution

    |

  8. A rod of length 12 cm moves with its ends always touching the coordina...

    Text Solution

    |

  9. A man running a race-course notes that the sum of the distances from t...

    Text Solution

    |

  10. Find the co-ordinates of the vertices, the foci, the eccentricity and ...

    Text Solution

    |

  11. Find the co-ordinates of the vertices, the foci, the eccentricity and ...

    Text Solution

    |

  12. Find the co-ordinates of the vertices, the foci, the eccentricity and ...

    Text Solution

    |

  13. Find the co-ordinates of the vertices, the foci, the eccentricity and ...

    Text Solution

    |

  14. Find the co-ordinates of the vertices, the foci, the eccentricity and ...

    Text Solution

    |

  15. Find the coordinates of the foci and the vertices, the ecentricity and...

    Text Solution

    |

  16. Find the co-ordinates of the vertices, the foci, the eccentricity and ...

    Text Solution

    |

  17. Find the co-ordinates of the vertices, the foci, the eccentricity and ...

    Text Solution

    |

  18. Find the lengths of transverse and conjugate axes, co-ordinates of foc...

    Text Solution

    |

  19. Find the lengths of transverse and conjugate axes, co-ordinates of foc...

    Text Solution

    |

  20. Find the lengths of transverse and conjugate axes, co-ordinates of foc...

    Text Solution

    |