Home
Class 12
MATHS
Find the locus of the centres of the cir...

Find the locus of the centres of the circle which cut the circles `x^2+y^2+4x-6y+9=0` and `x^2+y^2-5x+4y-2=0` orthogonally

A

`9x+10y-7=0`

B

`x-y+2=0`

C

`9x-10y-11=0`

D

`9x+10y+7=0`

Text Solution

Verified by Experts

The correct Answer is:
3
The locus of the center of the circle cutting `S_(1)=` and `S_(2)=` orthogonally is the radical axis between `S_(1)=0` and `S_(2)=`, i.e., `S_(1)-S_(2)=0` or `9x-10y+11=0`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Find the center of the smallest circle which cuts circles x^2+y^2=1 and x^2+y^2+8x+8y-33=0 orthogonally.

Equation of the circle which cuts the circle x^2+y^2+2x+ 4y -4=0 and the lines xy -2x -y+2=0 orthogonally, is

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

Find the angle at which the circles x^2+y^2+x+y=0 and x^2+y^2+x-y=0 intersect.

The centre of the smallest circle touching the circles x^2+ y^2-2y -3=0 and x^2 +y^ 2-8x -18y +93= 0 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.

The length of the common chord of the two circles x^2+y^2-4y=0 and x^2+y^2-8x-4y+11=0 is

Find the number of common tangents that can be drawn to the circles x^2+y^2-4x-6y-3=0 and x^2+y^2+2x+2y+1=0

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

The locus of the centre of a circle which touches externally the circle x^2 + y^2-6x-6y+14 = 0 and also touches Y-axis, is given by the equation (a) x^2-6x-10y+14 = 0 (b) x^2-10x-6y + 14 = 0 (c) y^2+6x-10y+14-0 (d) y^2-10x-6y + 14 = 0

CENGAGE-CIRCLE -Exercise (Single)
  1. P is a point (a , b) in the first quadrant. If the two circles which p...

    Text Solution

    |

  2. Find the number of common tangent to the circles x^2+y^2+2x+8y-23=0 an...

    Text Solution

    |

  3. Find the locus of the centres of the circle which cut the circles x^2+...

    Text Solution

    |

  4. Tangent are drawn to the circle x^2+y^2=1 at the points where it is me...

    Text Solution

    |

  5. If the line xcostheta+ysintheta=2 is the equation of a transverse comm...

    Text Solution

    |

  6. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Locus of thews of the centre of the circle which touches x^2+y^2 - 6x-...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. A circle C1 of radius b touches the circle x^2 + y^2 =a^2 externally a...

    Text Solution

    |

  17. Find the locus of centre of variable circle C, that rouches the circle...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |