Home
Class 12
MATHS
A focus of an ellipse is at the origin. ...

A focus of an ellipse is at the origin. The directrix is the line `x=4` and the eccenricityh is `1/2`, then length of semi-major axis is

A

`5//3`

B

`8//3`

C

`2//3`

D

`4//3`

Text Solution

Verified by Experts

The correct Answer is:
B
Since `a/e-ae=4` and `e=1/2`
`:.2a-a/2=4`
`implies a=8/3`
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 12

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos

  • PRACTICE SET 14

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos

Similar Questions

Explore conceptually related problems

A focus of an ellipse is at the origin.The directrix is the line x=4 and the eccentricity is (1)/(2) Then the length of the semi-major axis is

A focus of an ellipse is at the origin. The directrix is the line x""=""4 and the eccentricity is 1/2. Then the length of the semimajor axis is (1) 8/3 (2) 2/3 (3) 4/3 (4) 5/3

IF the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be 1/2 , then length of the minor axis is

If the distance betweent a focus and corresponding directrix of an ellipse be 8 and the eccentricity be 1/2, then length of the minor axis is

Let the distance between a focus and the corresponding directrix of an ellipse be 8 and the eccentricity be (1)/(2). If the length of the minor axis is k, then (sqrt(3)k)/(2) is

If question of the ellipse whose focus is (1,-1), then directrix the line x-y-3=0 and eccentricity 1/2 is

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 13-PAPER II OBJECTIVE TYPE
  1. If y=tan^(-1)[(sinx+cosx)/(cosx-sinx)] then (dy)/(dx) is

    Text Solution

    |

  2. The equation 12x^(2)+7xy-12y^(2)-18x+y+6=0 represents

    Text Solution

    |

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

    Text Solution

    |

  4. A parabola is drawn with focus at (3,4) and vertex at the focus of the...

    Text Solution

    |

  5. If a circle passes through (0,0) and (a,0) and (0,b), then the coordin...

    Text Solution

    |

  6. A line is drawn through the point P(3,11) to cut the circle x^(2)+y^(2...

    Text Solution

    |

  7. If the first, second and last terms of an arithmetic series are a,b, a...

    Text Solution

    |

  8. The denominator of a fraction is greater than 16 of the square of nume...

    Text Solution

    |

  9. The equation of tangent to the curve y=be^(-x//a) at the point where i...

    Text Solution

    |

  10. The function f(x)=x^(-x),(x epsilonR) attains a maximum value at x is

    Text Solution

    |

  11. The mean and varaince of binomial distribution are 4 and 3, respective...

    Text Solution

    |

  12. The value of lim(ntooo)[n/(n^(2)+1^(2))+n/(n^(2)+2^(2))+………….+n/(n^(...

    Text Solution

    |

  13. The value of int(-2)^(4)|x+1|dx is equal to

    Text Solution

    |

  14. The function f:""R""~""{0}vecR given by f(x)=1/x-2/(e^(2x)-1) ca...

    Text Solution

    |

  15. Define f on R into itself by f(x)={(x"sin"1/x, "when"x!=0),(0,"when"x=...

    Text Solution

    |

  16. If y=x-x^2, then the derivative of y^2 w.r.t x^2 is

    Text Solution

    |

  17. If f'(x)=g(x) and g'(x)=-f(x) for all x and f(2)=4=f'(2) then f^(2)(4)...

    Text Solution

    |

  18. The point on the curve y^(2)=x the tangent at which makes an angle 45^...

    Text Solution

    |

  19. The smallest circle with centre on Y-axis and passing through the poin...

    Text Solution

    |

  20. The function f(x)=x(x+3)e^(-(1/2)x) satisfies the conditions of Rolle'...

    Text Solution

    |