Home
Class 12
MATHS
If the length of a focal chord of the pa...

If the length of a focal chord of the parabola `y^2=4a x` at a distance `b` from the vertex is `c ,` then prove that `b^2c=4a^3`.

A

`a^(2) =bc`

B

`a^(3) =b^(2)c `

C

`b^(2) =ac`

D

`b^(2)c =4a^(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION-C ( Objective Type Questions ( More than one answer))|1 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION-C|44 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION - A)|55 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise section-J (Aakash Challengers Qestions)|13 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise section - J|6 Videos

Similar Questions

Explore conceptually related problems

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

If b and k are segments of a focal chord of the parabola y^(2)= 4ax , then k =

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 .

The length of focal chord to the parabola y^(2)=12x drawn from the point (3,6) on is __________ .

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

Length of the double ordinate of the parabola y^(2) = 4x , at a distance of 16 units from its vertex is

The length of a focal chord of the parabola y^2=4ax making an angle theta with the axis of the parabola is (a> 0) is :

Length of the focal chord of the parabola (y +3)^(2) = -8(x-1) which lies at a distance 2 units from the vertex of the parabola is (a) 8 (b) 6sqrt(2) (c) 9 (d) 5sqrt(3)

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

AAKASH INSTITUTE ENGLISH-CONIC SECTIONS-SECTION-B
  1. The vertex of the parabola y^(2) =(a-b)(x -a) is

    Text Solution

    |

  2. Two common tangents to the circle x^(2) + y^(2) = (a^(2))/(2) and the...

    Text Solution

    |

  3. If the length of a focal chord of the parabola y^2=4a x at a distance ...

    Text Solution

    |

  4. The point (a ,2a) is an interior point of the region bounded by the pa...

    Text Solution

    |

  5. If y+b=m1(x+a)and y+b=m2(x+a) are two tangents to the paraabola y^2=4a...

    Text Solution

    |

  6. The coordinates of a point on the parabola y^2=8x whose distance from ...

    Text Solution

    |

  7. If a circle intersects the parabola y^(2) = 4ax at points A(at(1)^(2),...

    Text Solution

    |

  8. If the line y - sqrt(3x)+3= 0 cuts line parabola y^(2) = x+2 at A and...

    Text Solution

    |

  9. Find the number of distinct normals that can be drawn from (-2,1) to t...

    Text Solution

    |

  10. If the chord of contact of tangents from a point P to the parabola y^2...

    Text Solution

    |

  11. The normal at any point P(t^(2), 2t) on the parabola y^(2) = 4x meets ...

    Text Solution

    |

  12. A ray of light moving parallel to x-axis gets reflected from a parabol...

    Text Solution

    |

  13. The vertex of the parabola y^2 = 8x is at the centre of a circle and t...

    Text Solution

    |

  14. The mirror image of the focus to the parabola 4(x + y) = y^(2) w.r.t....

    Text Solution

    |

  15. A tangent to the parabola y^2=8x makes an angle of 45^0 with the strai...

    Text Solution

    |

  16. Find the point on the curve y^2=4x which is nearest to the point (2, 1...

    Text Solution

    |

  17. The parametric coordinates of a point on the ellipse, whose foci are (...

    Text Solution

    |

  18. The number of values of c such that the straight line y=4x+c touches t...

    Text Solution

    |

  19. The locus of mid points of parts in between axes and tangents of ellip...

    Text Solution

    |

  20. The equation of the chord of the ellipse x^(2) + 4y^(2) = 4 having th...

    Text Solution

    |