Home
Class 12
MATHS
Through the vertex 'O' of parabola y^2=...

Through the vertex 'O' of parabola `y^2=4x`, chords OP and OQ are drawn at right angles to one another. Show that for all positions of P, PQ cuts the axis of the parabola at a fixed point. Also find the locus of the middle point of PQ.

Text Solution

Verified by Experts

The correct Answer is:
`(4, 0) ; y^(2) = 2(x - 4)`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - II|17 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 4 ( Level-II ) Previous Year (Paragraph)|2 Videos

  • PERMUTATION AND COMBINATION

    MOTION|Exercise EXAMPLE|23 Videos

Similar Questions

Explore conceptually related problems

Through the vertex 'O' of parabola y^(2)=4x chords OP and OQ are drawn at right angles to one another.Show that for all positions of P, PQ cuts the axis of the parabola at a fixixed point.Also find the locus of the middle point of PQ.

Through the vertex O of a parabola y^(2) = 4x chords OP and OQ are drawn at right angles to one another. Show that for all position of P, PQ cuts the axis of the parabola at a fixed point.

Through the vertex of the parabola y^(2)=4ax , chords OA and OB are drawn at right angles to each other . For all positions of the point A, the chord AB meets the axis of the parabola at a fixed point . Coordinates of the fixed point are :

Through the vertex O of the parabola y^(2)=4ax, variable chords O Pand OQ are drawn at right angles.If the variables chord PQ intersects the axis of x at R, then distance OR

If P is the point (1,0) and Q lies on the parabola y^(2)=36x , then the locus of the mid point of PQ is :

The vertex A of the parabola y^(2)=4ax is joined to any point P on it and PQ is drawn at right angles to AP to meet the axis in Q. Projection of PQ on the axis is equal to

If from the vertex of a parabola y^(2)=4x a pair of chords be drawn at right angles to one another andwith these chords as adjacent sides a rectangle be made,then the locus of the further end of the rectangle is

MOTION-PARABOLA-EXERCISE - III
  1. ‘O’ is the vertex of the parabola y^(2) = 4ax & L is the upper end of ...

    Text Solution

    |

  2. Through the vertex 'O' of parabola y^2=4x, chords OP and OQ are drawn...

    Text Solution

    |

  3. Find the equations of the chords of the parabola y^2= 4ax which pass t...

    Text Solution

    |

  4. Find the equations of the tangents to theparabola y= 16x, which are pa...

    Text Solution

    |

  5. Find the equation of tangents of the parabola y^2=12 x , which passes ...

    Text Solution

    |

  6. From vertex O ofthe parabola y^2=4ax perpendicular is drawn at a tange...

    Text Solution

    |

  7. Let P be a point on the parabola y^(2) - 2y - 4x+5=0, such that the ta...

    Text Solution

    |

  8. Two tangents to the parabola y^(2) = 8x meet the tangent at its vertex...

    Text Solution

    |

  9. Show that the normals at the points (4a, 4a) & at the upper end of t...

    Text Solution

    |

  10. In the parabola y^(2) = 4ax, the tangent at the point P, whose absciss...

    Text Solution

    |

  11. Prove that the locus of the middle point of portion of a normal to y^(...

    Text Solution

    |

  12. Three normals to y^2=4x pass through the point (15, 12). Show that one...

    Text Solution

    |

  13. Normals are drawn from a point P with slopes m1,m2 and m3 are drawn fr...

    Text Solution

    |

  14. Prove that, the normal to y^(2) = 12x at (3,6) meets the parabola agai...

    Text Solution

    |

  15. P & Q are the points of contact of the tangents drawn from the point T...

    Text Solution

    |

  16. A variable chord PQ of the parabola y^(2) = 4x is drawn parallel to th...

    Text Solution

    |

  17. Show that the normals at two suitable distinct real points on the para...

    Text Solution

    |

  18. Let S is the focus of the parabola y^(2) = 4ax and X the foot of the d...

    Text Solution

    |

  19. Prove that the parabola y^(2) = 16x and the circle x^(2) + y^(2) - 40x...

    Text Solution

    |

  20. .Find the equation ofthe circle which passes through the focus ofthe p...

    Text Solution

    |