Home
Class 12
MATHS
A point moves in such a manner that the ...

A point moves in such a manner that the sum of the squares of its distances from the origin and the point (2, -3) is always 19. Show that the locus of the moving point is a circle. Find the equation to the locus.

Text Solution

Verified by Experts

The correct Answer is:
`x^(2) + y^(2) - 2x + 3y - 3 = 0`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CHHAYA PUBLICATION|Exercise Exercise 3 (Long Answer Type Questions)|25 Videos

  • CIRCLE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (MCQs)|5 Videos

  • CIRCLE

    CHHAYA PUBLICATION|Exercise Exercise 3 (Very Short Answer Type Questions)|18 Videos

  • CALCULUS

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2014)|2 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVE EXAMS(Multiple Corrrect Answer type)|11 Videos

Similar Questions

Explore conceptually related problems

A point movs in such a manner that the sum of the squares of its distances from the points (a,0) and (-a, 0) is 2b^(2). Then the locus of the moving point is-

If the square of distance of a moving point from the point (2,0) is equal to 4 units , then the locus of the moving point is a -

A point moves so that the sum of squares of its distances from the points (1,2) and (-2,1) is always 6 . Then its locus is _

A point moves so that the sum of squares of its distances from the points (1, 2) and (-2, 1) is always 6. Then its locus is

A point moves so that sum of the squares of its distances from the vertices of a triangle is always constant. Prove that the locus of the moving point is a circle whose centre is the centroid of the given triangle.

What type of conic is the locus of the moving point (at^(2),2at) ? Find the equation of the locus .

A point moves so that the sum of squares of its distances from the points (1, 2) and (-2,1) is always 6. Then its locus is

A point moves on a plane in such a manner that the difference of distance from (3,0) is (3)/(2) times its distance from the line 3x - 4 = 0 , Show that the locus of the moving point is a hyperbola and the equation of its locus is 5x^(2) - 4y^(2) = 20 .

Find the locus of a point which moves so that the sum of the squares of its distances from the points (3,0) and (-3,0) is always equal to 50.

A point moves on a plane in such a manner that the difference of its distances from the points (4,0) and (-4,0) is always constant and equal to 4sqrt(2) show that the locus of the moving point is a rectangular hyperbola whose equation you are to determine.

CHHAYA PUBLICATION-CIRCLE-Exercise 3 (Short Answer Type Questions)
  1. A circle touches y-axis at (0, 5) and whose centre lies on the line 2x...

    Text Solution

    |

  2. Find the equation of a circle which passes through the point (4, 2) an...

    Text Solution

    |

  3. Two cirles of radii 2 and 10 units respectively pass through (2, 4) an...

    Text Solution

    |

  4. Prove that the point (-1, -2) lies on the circle x^(2) + y^(2) - x y -...

    Text Solution

    |

  5. Show that for all values of p, the circle x^(2) + y^(2) - x(3p+4) - y(...

    Text Solution

    |

  6. Find the coordinates of points equidistant from the axes and lying on ...

    Text Solution

    |

  7. Find the equation to the common chord of the two circles x^(2) + y^(2)...

    Text Solution

    |

  8. Find the equation of the common chord of the two circles x^(2)+y^(2)-4...

    Text Solution

    |

  9. Find the equation of the circles which passes through the origin and t...

    Text Solution

    |

  10. A point moves in such a manner that the sum of the squares of its dist...

    Text Solution

    |

  11. A(3, 0) and B(-3, 0) are two given points and P is a moving point : if...

    Text Solution

    |

  12. Show that the locus of the point of intersection of the lines x cos al...

    Text Solution

    |

  13. Whatever be the values of theta, prove that the locus of the point of ...

    Text Solution

    |

  14. Show that, x = (1)/(2)(3+5 cos theta), y = (1)/(2)(-4 + 5 sin theta) r...

    Text Solution

    |

  15. Prove that the square of the distance between the two points (x(1), y(...

    Text Solution

    |

  16. The equations of two diameters of a circle are x-2y+1 = 0 and x+y -2 =...

    Text Solution

    |

  17. Find the equation of the circle circumscribing the rectangle whose sid...

    Text Solution

    |

  18. A and B are two fixed points on a plane and P moves on the plane in su...

    Text Solution

    |

  19. Show that the equation of the circle described on the chord x cos alph...

    Text Solution

    |

  20. Find the circumcentre and circumradius of the triangle formed by the l...

    Text Solution

    |