Home
Class 12
MATHS
Find the equation of the ellipse whose e...

Find the equation of the ellipse whose eccentricity is `1/2`, one of the foci is (2, 3) and a directrix is x = 7. Also find the length of the major and minor axes of the ellipse.

Text Solution

Verified by Experts

The correct Answer is:
`(10)/(sqrt(3))`.
Promotional Banner

Topper's Solved these Questions

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY-II

    FULL MARKS|Exercise EXERCISE 5.1|12 Videos
  • TWO DIMENSIONAL ANALYTICAL GEOMETRY-II

    FULL MARKS|Exercise EXERCISE 5.2|8 Videos
  • THEORY OF EQUATIONS

    FULL MARKS|Exercise Additional Questions Solved|30 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the ellipse if centres is (3,-4) one of the foci is (3+sqrt(3), -4) and e= sqrt(3)/2

Find the equation of an ellipse whose eccentricity is 2/3, the latus rectum is 5 and the centre is at the origin.

Find the equation of the ellipse whose length of minor axis is 16 and foci are (0, +- 6) .

Find the equation of the ellipse whose one of the foci is (2,0) and the corresponding directrix is x = 8 and eccentricity is (1)/(2) .

Find the equation of the ellipse whose vertices are (+-13,0) and foci are (+-5,0)

Find the equation of the ellipse, whose length of the major axis is 20 and foci are (0,+-5)

Find the equation of parabola whose focus is (0,1) and the directrix is x+2=0. Also find the vertex of the parabola.

For the ellipse x^(2)+ 3y^(2) = a^(2) find the length of major and minor axis.

Consider two straight lines, each of which is tangent to both the circle x^2+y^2=1/2 and the parabola y^2=4x . Let these lines intersect at the point Q . Consider the ellipse whose center is at the origin O(0,\ 0) and whose semi-major axis is O Q . If the length of the minor axis of this ellipse is sqrt(2) , then which of the following statement(s) is (are) TRUE? For the ellipse, the eccentricity is 1/(sqrt(2)) and the length of the latus rectum is 1 (b) For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2 (c) The area of the region bounded by the ellipse between the lines x=1/(sqrt(2)) and x=1 is 1/(4sqrt(2))(pi-2) (d) The area of the region bounded by the ellipse between the lines x=1/(sqrt(2)) and x=1 is 1/(16)(pi-2)

FULL MARKS-TWO DIMENSIONAL ANALYTICAL GEOMETRY-II-Additional Question Solved
  1. Find the equation of the ellipse whose eccentricity is 1/2, one of the...

    Text Solution

    |

  2. find the equation of the circle with centre (2,3) and passing throu...

    Text Solution

    |

  3. Find the equation of a circle of radius 5 whose centre lies on x-axis ...

    Text Solution

    |

  4. Find the centre and radius of the following circles: x^(2)+y^(2)-2x+...

    Text Solution

    |

  5. Find the equation of the circles whose radius is 4 and whish is concen...

    Text Solution

    |

  6. Show that the four points (1,0), (2,-7), (8,1) and (9,-6) are concycli...

    Text Solution

    |

  7. Find the equation of a circle which passes through the points (1,-2) a...

    Text Solution

    |

  8. Find the equation (s) of the circle passing through the points (1,1) a...

    Text Solution

    |

  9. Find the equation of the ellipse if centres is (3,-4) one of the foci ...

    Text Solution

    |

  10. Find the equation of the hyperbola if centre (1,-2), length of the tra...

    Text Solution

    |

  11. Find axis, vertex focus and equation of directrix for y^(2)+8x-6y+1=0

    Text Solution

    |

  12. Find axis, Vertex, focus and equation of directrix for x^(2)-6x-12y-3=...

    Text Solution

    |

  13. Find the centre, eccentricity, foci, vertices of ellipse x^(2)+4y^(2)-...

    Text Solution

    |

  14. Find the eccentricity, centre, foci, vertices of 9x^(2)+4y^(2)=36

    Text Solution

    |

  15. Identify the type of conic section for each of the following equations...

    Text Solution

    |

  16. Find the eccentricity, centre, foci and vertices of the following hype...

    Text Solution

    |

  17. Identify the type of conic section for each of the following equations...

    Text Solution

    |

  18. Identify the type of conic section for each of the following equations...

    Text Solution

    |

  19. Identify the type of conic section for each of the following equations...

    Text Solution

    |

  20. Identify the type of conic section for each of the following equations...

    Text Solution

    |

  21. Identify the type of conic section for each of the following equations...

    Text Solution

    |