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 Exercise For Session 1|20 Videos
  • PARABOLA

    ARIHANT MATHS|Exercise Exercise For Session 2|25 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

Tangents at the end of focal chord are perpendicular to each other and meet at directrix

Prove that the tangents at the extremities of any chord make equal angles with the chord.

Through a point A on a circle,a chord AP is drawn & on the tangent at A a point T is taken such that AT=AP. If TP produced meet the diameter through A at Q,produced meet the limiting value of AQ when P moves upto A is double the diameter of the circle.

If S be the focus of the parabola and tangent and normal at any point P meet its axis in T and G respectively, then prove that ST=SG = SP .

the tangent drawn at any point P to the parabola y^(2)=4ax meets the directrix at the point K. Then the angle which KP subtends at the focus is

Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.

Consider the following statements : 1. The tangent of a circle is a line that meets the circle in one and only one point- 2. The tangent of a circle at the end point of the diameter is perpendicular to the diameter. Which of the above statemejita is/are correct ?

If angle subtended by any chord of a rectangular hyperbola at the centre is alpha and angle between the tangents at ends of chord is beta , then

The tangents at the end points of any chord through (1,0) to the parabola y^(2)+4x=8 intersect

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. Tangent to the curve y=x^2+6 at a point (1,7) touches the circle x^2+y...

    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 parabola is along the line y=x and the distance of its ver...

    Text Solution

    |

  5. The equations of the common tangents to the parabola y = x^2 and y=-...

    Text Solution

    |

  6. The locus of the vertices of the family of parabolas y =[a^3x^2]/3 + [...

    Text Solution

    |

  7. Angle between the tangents to the curve y=x^2-5x+6 at the points (2,0)...

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

    Text Solution

    |

  11. Statement I The curve y = x^2/2+x+1 is symmetric with respect to the l...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. A parabola has the origin as its focus and the line x=2 as the directr...

    Text Solution

    |

  15. The tangent PT and the normal PN to the parabola y^2=4ax at a point P...

    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. Consider the parabola y^2 = 8x. Let Delta1 be the area of the triangle...

    Text Solution

    |

  19. Let (x,y) be any point on the parabola y^2 = 4x. Let P be the point t...

    Text Solution

    |

  20. Let (x,y) be any point on the parabola y^2 = 4x. Let P be the point t...

    Text Solution

    |

  21. The shortest distance between line y-x=1 and curve x=y^2 is

    Text Solution

    |