Home
Class 11
MATHS
Show that the locus of a point that divi...

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.

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise EXERCISE|478 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

  • INFINITE SERIES

    MODERN PUBLICATION|Exercise EXAMPLE|10 Videos

Similar Questions

Explore conceptually related problems

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

Find the focus of the parabola x^2=4y

The vertex of the parabola y^2=4a(x+a) is:

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

The equation of tangent in slope form to the the parabola y^2 = 4x is

Find the area of the region enclosed by the parabola y^2 = 4x and the line y = 2x .

For the parabola 2y^2 = 5x , find the vertex, the axis and the focus.

The locus of the mid-point of the line segment joining the focus to a moving point oh the parabola y^2 = 4ax is a parabola with directrix :

The set of points on the axis of the parabola y^2-4x-2y+5=0 find the slope of normal to the curve at (0,0)

MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. A line is such that its segment between the straight line 5x-y-4=0 and...

    Text Solution

    |

  2. Straight lines : 3x + 4y = 5 and 4x- 3y = 15 intersect at the point A....

    Text Solution

    |

  3. Find the locus of a point whose sum of the distances from the origin a...

    Text Solution

    |

  4. Given vertices A (1, 1), B (4, -2) and C (5, 5) of a triangle, find th...

    Text Solution

    |

  5. If lines 5x + 12y-10 = 0 and 5x- 12y - 40 =0 touch a circle C1 of diam...

    Text Solution

    |

  6. Let S =x^2 + y^2 + 2gx + 2fy +c = 0 be a gives circle. Find the locus ...

    Text Solution

    |

  7. The points (1, 3) and (5, 1) are the opposite vertices of a rectangle....

    Text Solution

    |

  8. Let P(x1,y1) be a point and let ax + by +c =0 be a line. If L (h, k) i...

    Text Solution

    |

  9. Let P(x1,y1) be a point and let ax + by +c =0 be a line. If L (h, k) i...

    Text Solution

    |

  10. Let A be the centre of the circle x^2+y^2-2x-4y-20=0. If the tangents ...

    Text Solution

    |

  11. Find the equation of the circle passing through the point (0, 0) and t...

    Text Solution

    |

  12. Find the equation of the circle which touches the circle x^(2)+y^(2)-6...

    Text Solution

    |

  13. Three circles touch one another externally. The tangents at their poin...

    Text Solution

    |

  14. Find the centre and radius of the smaller of the two circles that touc...

    Text Solution

    |

  15. C1 and C2 are two concentric circles, the radius of C2 being twice tha...

    Text Solution

    |

  16. Show that the locus of a point that divides a chord of slope 2 of the ...

    Text Solution

    |

  17. From the point (-1, 2), tangent lines are drawn to the parabola y^2= 4...

    Text Solution

    |

  18. From a point A, common tangents are drawn to the circle x^2+y^2=a^2/2 ...

    Text Solution

    |

  19. Find the equatios of the tangents to the circle x^(2)+y^(2)=16 drawn f...

    Text Solution

    |

  20. Find the acute angle between the curves y=|x^(2)-1| and y=|x^(2)-3| at...

    Text Solution

    |