Home
Class 11
MATHS
Show that all chords of the curve 3x^2 -...

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 co-ordinates of the point.

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

Find the points on the curve x^2+y^2-2x-3 = 0 at which the tangents are parallel to the x-axis.

Find the condition that the chord of contact of tangents from the point (alpha, beta) to the circle x^2 + y^2 = a^2 should subtend a right angle at the centre. Hence find the locus of (alpha, beta) .

For the curve y = 4x^3-2x^5 , find all the points at which the tangent passes through the origin.

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 locus of the midpoint of a chord of the circle x^2+y^2=4 which subtends a right angle at the origins is (a) x+y=2 (b) x^2+y^2=1 (c) x^2+y^2=2 (d) x+y=1

Find the co-ordinates of the points on the curvey y = 2x^2 + 3x + 18 , the tangents at which pass through origin.

If a chord PQ of the parabola y^2 = 4ax subtends a right angle at the vertex, show that the locus of the point of intersection of the normals at P and Q is y^2 = 16a(x - 6a) .

MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. The equation of the hyperbola whose foci are (- 2, 0) and (2, 0) and e...

    Text Solution

    |

  2. Find the equation of the diagonal through the origin of the quadrilate...

    Text Solution

    |

  3. Show that all chords of the curve 3x^2 -y^2- 2x+ 4y= 0, which subtend ...

    Text Solution

    |

  4. A line is such that its segment between the straight line 5x-y-4=0 and...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |