Home
Class 12
MATHS
Prove that on the axis of any parabola t...

Prove that on the axis of any parabola there is a certain point 'k' which has the property that, if a chord PQ of parabola be drawn through it then `1/(PK)^2+1/(QK)^2` is the same for all positions of the chord.

Text Solution

Verified by Experts

The correct Answer is:
`1/(4a^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 semi-latus rectum of the parabola y^(2) = 4ax is the harmonic mean between the segments of any focal chord of the parabola.

The set of points on the axis of the parabola y^2-4x-2y+5=0 from which all the three normals to the parabola are real , is

Prove that of all chords of a circle through a given point within it, the least is one. Which is bisected at that point.

Find the equation of the parabola whose focus is at the point (1,2) and directrix is x+2y+3=0.

If the point ( at^2,2at ) be the extremity of a focal chord of parabola y^2=4ax then show that the length of the focal chord is a(t+1/t)^2 .

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

IF P_1P_2 and Q_1Q_2 two focal chords of a parabola y^2=4ax at right angles, then

Find the equation of the parabola which is symmetric about y-axis and passes through the point (2,-3) .

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that (t_2)^2geq8.

Show that the locus of a point that divides a chord of slope 2 of the parabola y^2= 4x internally in the ratio 1 : 2 is a parabola. Find the vertex of this parabola.

ARIHANT MATHS-PARABOLA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Prove that on the axis of any parabola there is a certain point 'k' wh...

    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

    |