Home
Class 11
MATHS
Length of the shortest normal chord of t...

Length of the shortest normal chord of the parabola `y^2=4ax` is

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Length of the shortest chord of the parabola y^2=4x+8 , which belongs to the family of lines (1+lambda)y+(lambda-1)x+2(1-lambda)=0 is

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

The locus of the point of intersection of tangents drawn at the extremities of a normal chord to the parabola y^2=4ax is the curve

The locus of the middle points of normal chords of the parabola y^2 = 4ax is-

The locus of the midpoints of the focal chords of the parabola y^(2)=4ax is

Tangents are drawn at the end points of a normal chord of the parabola y^(2)=4ax . The locus of their point of intersection is

The locus of the point of intersection of tangents drawn at the extremities of a focal chord to the parabola y^2=4ax is the curve

The harmonic mean of the segments of a focal chord of the parabola y^(2)=16ax, is

Find the locus of the midpoint of normal chord of parabola y^2=4ax

Prove that the locus of the middle points of all chords of the parabola y^2 = 4ax passing through the vertex is the parabola y^2 = 2ax .

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. t 1 and  t 2 are two points on the parabola y^...

    Text Solution

    |

  2. Tangent and normal are drawn at the point P-=(16 ,16) of the parabola ...

    Text Solution

    |

  3. Length of the shortest normal chord of the parabola y^2=4ax is

    Text Solution

    |

  4. The line x-y-1=0 meets the parabola y^2 = 4x at A and B. Normals at ...

    Text Solution

    |

  5. If normal are drawn from a point P(h , k) to the parabola y^2=4a x , t...

    Text Solution

    |

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

    Text Solution

    |

  7. An equilateral triangle S A B is inscribed in the parabola y^2=4a x ...

    Text Solution

    |

  8. min[(x1-x2)^2+(5+sqrt(1-x1^2)-sqrt(4x2))^2],AAx1,x2 in R , is (a)4sqr...

    Text Solution

    |

  9. The equation of the directrix of the parabola y^2+4y+4x+2=0 is (a)x=-1...

    Text Solution

    |

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

    Text Solution

    |

  11. At what point on the parabola y^2=4x the normal makes equal angle with...

    Text Solution

    |

  12. The focal chord to y^2=16 x is tangent to (x-6)^2+y^2=2. Then the poss...

    Text Solution

    |

  13. If the normals to the parabola y^2=4a x at three points P ,Q ,a n dR m...

    Text Solution

    |

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

    Text Solution

    |

  15. The curve described parametrically by x=t^2+t+1 , and y=t^2-t+1 repres...

    Text Solution

    |

  16. Statement 1: The line y=x+2a touches the parabola y^2=4a(x+a) Stateme...

    Text Solution

    |

  17. Consider a circle with its centre lying on the focus of the parabola, ...

    Text Solution

    |

  18. Normal drawn to y^2=4a x at the points where it is intersected by the...

    Text Solution

    |

  19. The radius of the circle touching the parabola y^2=x at (1, 1) and ha...

    Text Solution

    |

  20. Maximum number of common normals of y^2=4ax and x^2=4by is

    Text Solution

    |