Home
Class 12
MATHS
Prove that the radii of the circles x^(2...

Prove that the radii of the circles `x^(2)+y^(2)=1,x^(2)+y^(2)-2x-6y=6andx^(2)+y^(2)-4x-12y=9` are in AP.

Text Solution

Verified by Experts

The correct Answer is:
Hence, `r_(1),r_(2),r_(2)` are in AP.
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    ARIHANT MATHS|Exercise EXAMPLE|2 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise For Session 1|18 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

Similar Questions

Explore conceptually related problems

Prove that the centres of the circles x^2+y^2=1 , x^2+y^2+6x-2y-1=0 and x^2+y^2-12x+4y=1 are collinear

The radius and centre of the circles x^(2)+y^(2)=1,x^(2)+y^(2)+10y+24=0andx^(2)+y^(2)-8x+15=0 is

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

Find the radical centre of circles x^(2)+y^(2)+3x+2y+1=0,x^(2)+y^(2)-x+6y+5=0 and x^(2)+y^(2)+5x-8y+15=0 . Also find the equation of the circle cutting them orthogonally.

Show that the common chord of the circles x^(2)+y^(2)-6x-4y+9=0andx^(2)+y^(2)-8x-6y+23=0 paas through the centre of the second circle and find its length.

The centre of the circle x^(2)+y^(2)-6x+4y-1=0 is

The centres of 3 circles x^2+y^2 =1, x^2+y^2 +6x-2y=1, x^2+y^2-12x+4y=1 are :

Prove that the centres of the three circles : x^2 + y^2 -4x-6y-14=0, x^2 + y^2+ 2x+4y-5=0 and x^2 + y^2-10x -16y + 7 = 0 are collinear.

Prove that the circles x^(2) +y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(2) - 10x - 6y + 14 = 0 touch at the point (3,-1)

Find the angle between the circles S:x^(2)+y^(2)-4x+6y+11=0andS':x^(2)+y^(2)-2x+8y+13=0

ARIHANT MATHS-CIRCLE -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Prove that the radii of the circles x^(2)+y^(2)=1,x^(2)+y^(2)-2x-6y=6a...

    Text Solution

    |

  2. Find the derivative of (a/x^4 - b/x^2 + cosx)

    Text Solution

    |

  3. If the circles x^2+y^2+2a x+c y+a=0 and points Pa n dQ , then find the...

    Text Solution

    |

  4. A circle touches the x-axis and also touches the circle with center (0...

    Text Solution

    |

  5. Find the derivative of (4x - 2)

    Text Solution

    |

  6. Let ABCD be a square of side length 2 units. C2 is the circle through ...

    Text Solution

    |

  7. ABCD is a square of side length 2 units. C(1) is the circle touching ...

    Text Solution

    |

  8. ABCD is a square of side length 2 units. C(1) is the circle touching ...

    Text Solution

    |

  9. If the lines 3x-4y-7=0 and 2x-3y-5=0 are two diameters of a circle of ...

    Text Solution

    |

  10. Let C be the circle with centre (0, 0) and radius 3 units. The equatio...

    Text Solution

    |

  11. Find the derivative of (ax + b)^n

    Text Solution

    |

  12. Consider a family of circles which are passing through the point (-1,1...

    Text Solution

    |

  13. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

    Text Solution

    |

  14. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

    Text Solution

    |

  15. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

    Text Solution

    |

  16. Consider: L1:2x+3y+p-3=0 L2:2x+3y+p+3=0 where p is a real number and...

    Text Solution

    |

  17. The point diametrically opposite to the point P(1, 0) on the circle x^...

    Text Solution

    |