Home
Class 12
MATHS
The minimum radius of the circle which c...

The minimum radius of the circle which contains the three circles, `x^(2)+y^(2)-4y-5=0,x^(2)+y^(2)+12x+4y+31=0` and `x^(2)+y^(2)+6x+12y+36=0` is

A

`(7)/(18)sqrt(900)+3`

B

`(sqrt(845))/(9)+4`

C

`(5)/(36)sqrt(949)+3`

D

none of these

Text Solution

AI Generated Solution

The correct Answer is:
To find the minimum radius of the circle that contains the three given circles, we can follow these steps: ### Step 1: Identify the equations of the circles The equations of the circles are given as: 1. \( x^2 + y^2 - 4y - 5 = 0 \) 2. \( x^2 + y^2 + 12x + 4y + 31 = 0 \) 3. \( x^2 + y^2 + 6x + 12y + 36 = 0 \)
To find the minimum radius of the circle that contains the three given circles, we can follow these steps: ### Step 1: Identify the equations of the circles The equations of the circles are given as: 1. \( x^2 + y^2 - 4y - 5 = 0 \) 2. \( x^2 + y^2 + 12x + 4y + 31 = 0 \) 3. \( x^2 + y^2 + 6x + 12y + 36 = 0 \)
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CENGAGE ENGLISH|Exercise Multiple Correct Anser Type|29 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise Linked Comprehension Type (For Problem 1-3)|3 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 4.20|1 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Matrix|4 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

Similar Questions

Explore conceptually related problems

The two circles x^(2)+y^(2)-5=0 and x^(2)+y^(2)-2x-4y-15=0

The equation of circle of minimum radius which contacts the three circle x^2 + y^2 -4y-5 = 0, x^2 +y^2 +12x +4y +31 = 0, x^2 +y^2 + 6x +12y + 36 = 0 then the radius of given circle is (l + m/36sqrt949) then the value of l + m is :

The circle x^(2)+y^(2)-4x-6y-12=0, x^(2)+y^(2)+6x-8y+21=0 are

The equation of the circle which cuts orthogonally the three circles x^2+y^2+4x+2y+1=0, 2x^2+2y^2+8x+6y-3=0, x^2+y^2+6x-2y-3=0 is

The circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+4x+6y+4=0

The circles x^(2)+y^(2)-12x+8y+48=0, x^(2)+y^(2)-4x+2y-4=0 are

The equation of the circle which cuts the three circles x^2+y^2-4x-6y+4=0, x^2+y^2-2x-8y+4=0, x^2+y^2-6x-6y+4=0 orthogonally is

Find the equation of the circle which cuts the three circles x^2+y^2-3x-6y+14=0,x^2+y^2-x-4y+8=0, and x^2+y^2+2x-6y+9=0 orthogonally.

Let circle cuts ortholognally each of the three circles x^(2) + y^(2) + 3x + 4y + 11 = 0, x^(2) + y^(2) - 3x + 7y - 1 = 0 and x^(2) + y^(2) + 2x = 0

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.

CENGAGE ENGLISH-CIRCLE -Excercises (Single Correct Answer Type)
  1. Tangent are drawn to the circle x^2+y^2=1 at the points where it is me...

    Text Solution

    |

  2. If the line xcostheta=2 is the equation of a transverse common tangent...

    Text Solution

    |

  3. Let C1 and C2 are circles defined by x^2+y^2 -20x+64=0 and x^2+y^2+...

    Text Solution

    |

  4. The circles having radii r1a n dr2 intersect orthogonally. The length ...

    Text Solution

    |

  5. The two circles which pass through (0,a)a n d(0,-a) and touch the line...

    Text Solution

    |

  6. Locus of the centre of the circle which touches x^2+y^2 - 6x-6y+14 =0 ...

    Text Solution

    |

  7. If the chord of contact of tangents from a point P to a given circle p...

    Text Solution

    |

  8. If the angle of intersection of the circle x^2+y^2+x+y=0 and x^2+y^2+x...

    Text Solution

    |

  9. The coordinates of two points Pa n dQ are (x1,y1)a n d(x2,y2)a n dO is...

    Text Solution

    |

  10. If the circumference of the circle x^2 + y^2 + 8x + 8y - b = 0 is bise...

    Text Solution

    |

  11. Equation of the circle which cuts the circle x^2+y^2+2x+ 4y -4=0 and ...

    Text Solution

    |

  12. The minimum radius of the circle which contains the three circles, x^...

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. If a circle passes through the point (a, b) and cuts the circle x^2 + ...

    Text Solution

    |

  15. The centre of the smallest circle touching the circles x^2+ y^2-2y -3=...

    Text Solution

    |

  16. Two circle with radii r(1) and r(2) respectively touch each other exte...

    Text Solution

    |

  17. Consider points A(sqrt13,0) and B(2sqrt13,0) lying on x-axis. These po...

    Text Solution

    |

  18. The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing ...

    Text Solution

    |

  19. If the circumference of the circle x^2+y^2+8x+8y-b=0 is bisected by th...

    Text Solution

    |

  20. The equation of the circle passing through the point of intersection o...

    Text Solution

    |