Home
Class 11
MATHS
vertex and focus of a parabola are (-1,1...

vertex and focus of a parabola are (-1,1) and (2,3) respectively. find the equation of the directrix.

Text Solution

Verified by Experts

Let the line through the focus `F` and the vertex `V` (this is the axis of the parabola) meet the directrix in the point `P` (i.e. `P` is the foot of the perpendicular from `V` to the directrix).
As `V` is the midpoint of `FP`: `P - V = V - F`
`=> P = 2V - F = ( 2×(-1) - 2 , 2×1 - 3 ) = ( -4, -1 )` ...
Promotional Banner

Topper's Solved these Questions

  • MEASUREMENT OF ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|56 Videos

  • PERMUTATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|287 Videos

Similar Questions

Explore conceptually related problems

If the vertex and focus of a parabola are (2,1) and (1,-1) then its equation is

If the vertex and focus of a parabola are (2,1) and (1,-1) then its equation is

If the focus and the vertex of a parabola are (2,3) and (-1,1) respectively, then the directrix is :

Find the equation of the parabola with vertex at (0,0) and focus at (0,2) Also, find the equation of its directrix.

If the focus of a parabola is (-2,1) and the directrix has the equation x+y=3 then its vertex is a.(0,3) b.(-1,1/2) c.(-1,2) d.(2,-1)

The focus and directrix of a parabola are (1,2) and 2x-3y+1=0 .Then the equation of the tangent at the vertex is

The focus and directrix of a parabola are (1,2) and 2x-3y+1=0 .Then the equation of the tangent at the vertex is

If the focus of the parabola is (-2,1) and the directrix has the equation x+y=3 then the vertex is

The focus of a parabola is (1,2) and the point of intersection of the directrix and axis is (2,3).Then the equation of the parabola is

If focus and vertex of a parabola are respectively (1,-1) and (2,1), then its directrix is

RD SHARMA-PARABOLA-Solved Examples And Exercises
  1. If the parabola y^2=4a x\ passes through the point (3,2) then find th...

    Text Solution

    |

  2. If the vertex of a parabola is the point (-3,0) and the directrix is t...

    Text Solution

    |

  3. The coordinates of the focus of the parabola y^2-x-2y+2=0 are a. (5/4...

    Text Solution

    |

  4. The vertex of the parabola (y+a)^2=8a(x-a) is a.(-a ,-a) b. (a ,-a) c....

    Text Solution

    |

  5. If the focus of a parabola is (-2,1) and the directrix has the equatio...

    Text Solution

    |

  6. The equation of the parabola whose vertex is (a ,0) and the directrix ...

    Text Solution

    |

  7. The parametric equations of a parabola are x=t^2+1, y=2t+1. The Cartes...

    Text Solution

    |

  8. vertex and focus of a parabola are (-1,1) and (2,3) respectively. find...

    Text Solution

    |

  9. The equation of the directrix of the parabola whose vertex and focus a...

    Text Solution

    |

  10. If V and S are respectively the vertex and focus of the parabola y^2+6...

    Text Solution

    |

  11. The directrix of the parabola x^2-4x-8y + 12=0 is

    Text Solution

    |

  12. The equation of the parabola with focus (0,0) and directrix x+y=4 is a...

    Text Solution

    |

  13. The line 2x−y+4=0 cuts the parabola y^2=8x in P and Q. The mid-point o...

    Text Solution

    |

  14. In the parabola y^2=4a x , the length of the chord pasing through the ...

    Text Solution

    |

  15. The length of the latus rectum of the parabola y^2+8x-2y+17=0 is a.2 b...

    Text Solution

    |

  16. The vertex of the parabola (y-2)^2=16(x-1) is a.(1,2) b.(-1,2) c. (1,-...

    Text Solution

    |

  17. The length of latus rectum of the parabola 4y^2+2x−20y+17=0 is (a) 3 (...

    Text Solution

    |

  18. The focus of the parabola y=2x^2+x is a.(0,0) b. (1//2,1//4) c. (-1//4...

    Text Solution

    |

  19. Which of the following points lie on the parabola x^2=4a y ? a.x=a t^...

    Text Solution

    |

  20. The equation of the parabola whose focus is (1,-1) and the directrix i...

    Text Solution

    |