Home
Class 11
MATHS
If two normals to a parabola y^2 = 4ax i...

If two normals to a parabola `y^2 = 4ax` intersect at right angles then the chord joining their feet pass through a fixed point whose co-ordinates are:

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

A normal chord of the parabola y^2=4ax subtends a right angle at the vertex, find the slope of chord.

If a , b , c are in A . P ., then the straight line ax + 2 by + c = 0 will always pass through a fixed point whose coordinates are _

If a+b+c=0, then the straight lines 4ax + 3by+c=0 always pass through a fixed whose coordinates are-

Show that all chords of the curve 3x^2-y^2-2x+4y=0, which subtend a right angle at the origin, pass through a fixed point. Find the coordinates of the point.

Tangents are drawn from the points on the line x−y−5=0 to x^2+4y^2=4 , then all the chords of contact pass through a fixed point, whose coordinate are

If a normal to a parabola y^2 =4ax makes an angle phi with its axis, then it will cut the curve again at an angle

If the angle between the normal to the parabola y^(2)=4ax at point P and the focal chord passing through P is 60^(@) , then find the slope of the tangent at point P.

Normals are drawn at points A, B, and C on the parabola y^2 = 4x which intersect at P. The locus of the point P if the slope of the line joining the feet of two of them is 2, is

If a + 2b + 3c = 0, the family of straight lines ax + by + c = 0 passes through a fixed point, find the co-ordinates of fixed point.

A quadrilateral is inscribed in a parabola y^2=4a x and three of its sides pass through fixed points on the axis. Show that the fourth side also passes through a fixed point on the axis of the parabola.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Tangent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the ...

    Text Solution

    |

  2. PQ is a normal chord of the parabola y^2 =4ax at P, A being t...

    Text Solution

    |

  3. If two normals to a parabola y^2 = 4ax intersect at right angles then ...

    Text Solution

    |

  4. If the normals to the parabola y^2=4a x at P meets the curve again at ...

    Text Solution

    |

  5. If a leaf of a book is folded so that one corner moves along an opp...

    Text Solution

    |

  6. A parabola of latus-rectum 1 touches a fixed equal parabola. The axe...

    Text Solution

    |

  7. A movable parabola touches x-axis and y-axis at (0,1) and (1,0). Then ...

    Text Solution

    |

  8. Let N be the foot of perpendicular to the x-axis from point P on the p...

    Text Solution

    |

  9. Two lines are drawn at right angles, one being a tangent to y^(2)=4ax ...

    Text Solution

    |

  10. The area of the trapezium whose vertices lie on the parabola y^2 = 4x ...

    Text Solution

    |

  11. Find the range of parameter a for which a unique circle will pass thro...

    Text Solution

    |

  12. Find the radius of the largest circle, which passes through the focus ...

    Text Solution

    |

  13. A tangent is drawn to the parabola y^(2)=4ax at P such that it cuts th...

    Text Solution

    |

  14. Tangents are drawn to the parabola at three distinct points. Prove t...

    Text Solution

    |

  15. Statement 1: The circumcircle of a triangle formed by the lines x=0,...

    Text Solution

    |

  16. Statement 1: The point of intersection of the tangents at three dist...

    Text Solution

    |

  17. Statement 1: If the straight line x=8 meets the parabola y^2=8x at Pa ...

    Text Solution

    |

  18. Statement 1: Normal chord drawn at the point (8, 8) of the parabola ...

    Text Solution

    |

  19. Statement 1: The value of alpha for which the point (alpha,alpha^2) li...

    Text Solution

    |

  20. Statement 1: If there exist points on the circle x^2+y^2=a^2 from whic...

    Text Solution

    |