Home
Class 11
MATHS
Prove that the radii of circles x^2 + y^...

Prove that the radii of circles `x^2 + y^2 = 1, x^2 + y^2 - 2x -6y = 6` and `x^2 + y^2 - 4x - 12y = 9` are in A.p.

Promotional Banner

Topper's Solved these Questions

  • CARTESIAN COORDINATES AND STRAIGHT LINE

    PATHFINDER|Exercise QUESTION BANK|249 Videos

  • COMPLEX NUMBER

    PATHFINDER|Exercise QUESTION BANK|224 Videos

Similar Questions

Explore conceptually related problems

Prove that the centres of the three circles x^(2) + y^(2) - 2x + 6y + 1 = 0, x^(2) + y^(2) + 4x - 12y + 9 = 0 and x^(2) + y^(2) - 16 = 0 are collinear.

The circle x^2 + y^2 - 2x - 4y + 1 = 0 and x^2 + y^2 + 4x + 4y - 1 = 0

Show that the centres of the following circles lie on a line and their radii are in A.P. : x^(2) + y^(2) = 1, x^(2) + y^(2) + 6x - 2y -6 = 0, x^(2) + y^(2) - 12x + 4y - 9 = 0 .

Prove that the centres of the circles x^(2) + y^(2) - 10x + 9 = 0, x^(2) + y^(2) - 6x + 2y + 1 = 0 and x^(2) + y^(2) - 18x - 4y + 21 = 0 lie on a line, find the equation of the line on which they lie.

Find the equation to the common chord of the two circles x^(2) + y^(2) - 4x + 6y - 36 = 0 and x^(2) + y^(2) - 5x + 8y - 43 = 0 .

Center of the circle x^(2) + y^(2) - 4x + 6y - 12 = 0 is -

A circle through the common points of the circles x^(2) + y^(2) - 2x - 4y + 1 = 0 and x^(2) + y^(2) - 2x - 6y + 1 = 0 has its centre on the line 4x - 7y - 19 = 0 . Find the centre and radius of the circle .

Center of the circle x^(2) + y^(2) - 6x + 4y - 12 = 0 is -

Show that the circles x^(2) + y^(2) + 6x + 2y + 8 = 0 and x^(2) + y^(2) + 2x + 6y + 1 = 0 intersect each other.

Find the length of the common chord of the circles x^2+y^2+2x+6y=0 and x^2+y^2-4x-2y-6=0

PATHFINDER-CIRCLE-QUESTION BANK
  1. Prove that the radii of circles x^2 + y^2 = 1, x^2 + y^2 - 2x -6y = 6 ...

    Text Solution

    |

  2. Find the equation of the circle whose centre is the point of intersect...

    Text Solution

    |

  3. A circle has radius 3 units and its centre lies on the line y = x - 1....

    Text Solution

    |

  4. Find the area of an equilateral triangle inscribed in the circle x^2 +...

    Text Solution

    |

  5. Find the equation of the circle which passes through the point (2, -2)...

    Text Solution

    |

  6. Find the equation of the circle whose diameter is the line joining the...

    Text Solution

    |

  7. A circle of radius 2 lies in the first quadrant and touches both the a...

    Text Solution

    |

  8. A circle of radius 5 units touches co-ordinates axes the first quadra...

    Text Solution

    |

  9. Find the length of tangents drawn from the point (3, -4) to the circle...

    Text Solution

    |

  10. The chord of contact of tangents drawn from a point on the circle x^2 ...

    Text Solution

    |

  11. Find the equation of the circle which touches the positive y-axis at a...

    Text Solution

    |

  12. Find the equation of the circle which passes through the origin and cu...

    Text Solution

    |

  13. Find the point(s) of intersection of the line 2x + 3y = 18 and the cir...

    Text Solution

    |

  14. Obtain the locus of the point of intersection of the tangent to the ci...

    Text Solution

    |

  15. A and B are two points in xy-plane, which are 2sqrt2 units distance ap...

    Text Solution

    |

  16. Two circles each of radius 5 units touch each at (1, 2) If the equati...

    Text Solution

    |

  17. One of the diameters of the circle circumscribing the rectangle ABCD i...

    Text Solution

    |

  18. Find the locus of the mid points of the chords of the circle x^2 + y^2...

    Text Solution

    |

  19. The centre of the circle S = 0 lies on the line 2x -2y + 9 = 0 and S =...

    Text Solution

    |

  20. The tangents to x^2+y^2=a^2 having inclinations alpha and beta interse...

    Text Solution

    |