Home
Class 12
MATHS
The locus of the midpoint of the segment...

The locus of the midpoint of the segment joining the focus to a moving point on the parabola `y^2=4a x` is another parabola with directrix `y=0` (b) `x=-a` `x=0` (d) none of these

A

x=-a

B

x=-a/2

C

x=0

D

x=a/2

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    MOTION|Exercise EXERCISE - II|17 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - III|25 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 4 ( Level-II ) Previous Year (Paragraph)|2 Videos

  • PERMUTATION AND COMBINATION

    MOTION|Exercise EXAMPLE|23 Videos

Similar Questions

Explore conceptually related problems

The locus of the mid-point of the line segment joning the focus to a moving point on the parabola y^(2)=4ax is another parabola with directrix

The locus of the midpoint of the segment joining the focus to a moving point on the parabola y^(2)=4ax is another parabola with directrix y=0 (b) x=-ax=0 (d) none of these

The locus of the midpoint of the line segment joining the focus to a moving point on the parabola y^(2)=4ax is another parabola whose (a) Directrix is y-axis (b) Length of latus rectum is 2a (c)focus is ((a)/(2),0) (d) Vertex is (a,0)

The locus of a point which divides the line segment joining the point (0, -1) and a point on the parabola, x^(2) = 4y internally in the ratio 1: 2, is:

The locus of the midpoint of the focal distance of a variable point moving on theparabola y^(2)=4ax is a parabola whose (d)focus has coordinates (a,0)(a)latus rectum is half the latus rectum of the original parabola (b)vertex is ((a)/(2),0) (c)directrix is y-axis.

Find the focus and directrix of the parabola 3x^2 + 12x + 8y=0 .

The directrix of the parabola y^(2)+4x+3=0 is

MOTION-PARABOLA-EXERCISE - I
  1. let P be the point (1, 0) and Q be a point on the locus y^2= 8x. The l...

    Text Solution

    |

  2. Let N be the foot of perpendicular to the x-axis from point P on the p...

    Text Solution

    |

  3. The locus of the midpoint of the segment joining the focus to a moving...

    Text Solution

    |

  4. If (t^2, 2t) is one end ofa focal chord of the parabola, y^2=4x then ...

    Text Solution

    |

  5. Find the locus of the point of intersection of the perpendicular ta...

    Text Solution

    |

  6. Find the common tangent of x^(2) + y^(2) = 2a^(2) and y^(2) = 8ax.

    Text Solution

    |

  7. The tangents to the parabola x = y^2 + c from origin are perpendicular...

    Text Solution

    |

  8. T P and T Q are tangents to the parabola y^2=4a x at Pa n dQ , respect...

    Text Solution

    |

  9. P Q is a normal chord of the parabola y^2=4a x at P ,A being the verte...

    Text Solution

    |

  10. The normal at the point (bt1^2, 2bt1) on the parabola y^2 = 4bx meets ...

    Text Solution

    |

  11. Locus of the intersection of the tangents at the ends of the normal ch...

    Text Solution

    |

  12. If the normal chhord of the parabola y^(2)=4x makes an angle 45^(@) wi...

    Text Solution

    |

  13. If x+y=k is normal to y^2=12 x , then k is 3 (b) 9 (c) -9 (d) -3

    Text Solution

    |

  14. Tangents are drawn from the points on the line x-y+3=0 parabola y^2=8x...

    Text Solution

    |

  15. The line 4x-7y + 10 = 0 intersects the parabola, y^2 = 4x at the point...

    Text Solution

    |

  16. From the point (4, 6) a pair of tangent lines are drawn to the parabol...

    Text Solution

    |

  17. PSQ is a focal chord of the parabola y^2=8xdotIf\ S P=6, then write SQ...

    Text Solution

    |

  18. The equation of the circle drawn with the focus of the parabola (x – 1...

    Text Solution

    |

  19. The slope of the focal chords of the parabola y^(2) = 16x which are ta...

    Text Solution

    |

  20. The equation of the common tangent touching the circle (x-3)^2+y^2=9 a...

    Text Solution

    |