Home
Class 12
MATHS
If the diameter through any point P of a...

If the diameter through any point P of a parabola meets any chord in A and the tangent at the end of the chord meets the diameter in B and C, then prove that `PA^2=PB.PC`

Text Solution

Verified by Experts

The correct Answer is:
`=PB. PC`
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

If the tangent at any point P of a curve meets the axis of X in T find the curve for which O P=P T ,O being the origin.

TP and TQ are any two tangents to a parabola and the tangent at a third point R cuts them in P' and Q' . Prove that (TP')/(TP)+(TQ')/(TQ)=1

Find a point on the parabola f(x) = (x - 3)^2 , where the tangent is parallel to the chord joining the points (3, 0) and (4, 1).

The tangent at the point P of a rectangular hyperbola meets the asymptotes at L and M and C is the centre of the hyperbola. Prove that PL=PM=PC .

Find a point on the parabola y = (x-3)^2 , where the tangent s parallel to the chord joining (3,0) and (4,1)

Find a point on the parabola y = (x-2)^2 , where the tangent is parallel to the chord joining (2,4) and (4,4)

In two chords AB and CD intersect each AB and CD intersect each other at the point P. Prove that AP. PB = CP . DP

Through a point P(h,k,l) a plane is drawn at righat angle to OP to meet the coordinate axes in A,B and C . If OP =p show that the area of /_\ABC is p^5/(2hkl)

Find the equation of a curve passing through the point (1,1), if the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid point of AB.

Of all the line segments drawn from a point P to a line l not containing P, let PD be the shortest. If B and C are points on l such that D is the mid-point of BC, prove that PB = PC.

ARIHANT MATHS-PARABOLA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If the diameter through any point P of a parabola meets any chord in A...

    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

    |