Home
Class 12
MATHS
Prove that the length of a focal chord o...

Prove that the length of a focal chord of a parabola varies inversely as the square of its distance from the vertex.

Text Solution

Verified by Experts

The correct Answer is:
`implies 1inpropto1/d^2`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    ARIHANT MATHS|Exercise JEE type solved examples|1 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise For Session 1|20 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

Similar Questions

Explore conceptually related problems

Prove that the perpendicular focal chords of a rectangular hyperbola are equal.

Prove that the equation of the parabola whose vertex and focus are on the X-axis at a distance a and a'from the origin respectively is y^2=4(a'-a)(x-a)

The centripriptal acceleration of a particle varies inversely with the square of the radius r of the circular path.the KE of the particle varies directly as :

The length of a chord of circle of radius 10 cm is 12 cm. Determine the distance of the chord from the centre.

Prove that the normal chord to a parabola at the point whose ordinate is equal to the abscissa subtends a right angle at the focus.

The volume of a cube is increasing at a constant rate. Prove that the increase in its surface area varies inversely as the length of the side.

Statement I: The lines from the vertex to the two extremities of a focal chord of the parabola y^2=4ax are perpendicular to each other. Statement II: If the extremities of focal chord of a parabola are (at_1^2,2at_1) and (at_2^2,2at_2) , then t_1t_2=-1 .

Statement 1: The length of focal chord of a parabola y^2=8x making on angle of 60^0 with the x-axis is 32. Statement 2: The length of focal chord of a parabola y^2=4a x making an angle with the x-axis is 4acos e c^2alpha

If the electric force varies inversely as the cube of the distance, will the Gauss's law hold good?

Prove that sum of squares of the diagonals of a parallelogram is equal to sum of squares of its sides.

ARIHANT MATHS-PARABOLA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Prove that the length of a focal chord of a parabola varies inversely ...

    Text Solution

    |

  2. Let A and B be two finite sets such that n(A) =85, n(B) = 65and n(A ∪ ...

    Text Solution

    |

  3. Let P be the point (1,0) and Q be a point on the locus y^(2)=8x. The l...

    Text Solution

    |

  4. The axis of a parabola is along the line y=x and the distance of its v...

    Text Solution

    |

  5. In a school, all pupils play either Hockey or Football or both. 400 pl...

    Text Solution

    |

  6. The locus of the vertex of the family of parabolas y=(a^3x^2)/3+(a^(2x...

    Text Solution

    |

  7. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

    Text Solution

    |

  8. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  9. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  10. Find slope of tangent to the curve if equation is x^2 + y^2 = 9

    Text Solution

    |

  11. Statement 1 : The curve y=-(x^2)/2+x+1 is symmetric with respect to th...

    Text Solution

    |

  12. The equation of a tangent to the parabola y^2=""8x""i s""y""=""x""+"...

    Text Solution

    |

  13. Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0. Then,

    Text Solution

    |

  14. If a parabola has the origin as its focus and the line x = 2 as the ...

    Text Solution

    |

  15. In a school, there are 30 teachers who teach Mathematics or Physics. O...

    Text Solution

    |

  16. Let A and B be two distinct points on the parabola y^2=4x. If the ax...

    Text Solution

    |

  17. If two tangents drawn from a point P to the parabola y2 = 4x are at ri...

    Text Solution

    |

  18. Of the 125 students in an elementary school, 89 students play checkers...

    Text Solution

    |

  19. What is the 5th term of this sequence 9, 13, 17, ...?

    Text Solution

    |

  20. In a group of 400 people, 250 can speak Punjabi and 200 can speak Engl...

    Text Solution

    |

  21. If f (x) = a cos (bx + c) + d, then what is the range of f (x)?

    Text Solution

    |