Home
Class 12
MATHS
If P and Q are conjugate points w.r.t a ...

If P and Q are conjugate points w.r.t a circle `S=x^2+y^2+2gx+2fy+c=0` , then prove that the circle PQ as diameter cuts the circles S=0 orthogonallly.

Promotional Banner

Topper's Solved these Questions

  • SYSTEM OF CIRCLES

    AAKASH SERIES|Exercise Additional Solved Examples|8 Videos
  • SYSTEM OF CIRCLES

    AAKASH SERIES|Exercise Exercise -2.1 (Short Answer)|11 Videos
  • SYSTEM OF CIRCLES

    AAKASH SERIES|Exercise EXERCISE 2.2|22 Videos
  • STRAIGHT LINES (3D)

    AAKASH SERIES|Exercise PRACTICE EXERCISE|28 Videos
  • THEORY OF EQUATIONS

    AAKASH SERIES|Exercise EXERCISE-III|46 Videos

Similar Questions

Explore conceptually related problems

If A and B are conjugate points w.r.t to circle x^(2)+y^(2)=r^(2) then OA^(2)+OB^(2)=

If kx+3y=1, 2x+y+5=0 are conjugate liens w.r.t the circle x^(2)+y^(2)-2x-4y-4=0 then k=

Show that (-6,1) and (2,3) are conjugate points w.r.t. the circle x^(2) + y^(2) -2x+2y+1=0

Show that (-6,1) and (2,3) are conjugate points w.r.t. the circle x^(2) + y^(2) -2x+2y+1=0

The points A(2, 3) and B(-7, -12) are conjugate points w.r.t to the circle x^2 + y^2 - 6x - 8y - 1 = 0 . The centre of the circle passing through A and B and orthogonal to given circle is

If 3x+2y=3 and 2x+5y=1 are conjugate lines w.r.t the circle x^(2)+y^(2)=r^(2) then r^(2)=

Polar of the origin w.r.t. the circle x^2+y^2+2ax+2by+c=0 touches the circle x^(2)+y^(2)=r^(2) if

AAKASH SERIES-SYSTEM OF CIRCLES-Solved Examples
  1. If the the angle between the circles x^2+y^2-12x-6y+41=0 and x^2+y^...

    Text Solution

    |

  2. Find the equation of the circle which passes through the point (0,-3) ...

    Text Solution

    |

  3. If P and Q are conjugate points w.r.t a circle S=x^2+y^2+2gx+2fy+c=0 ,...

    Text Solution

    |

  4. If the equations of two circles whose radii are a and a' are S=0 and S...

    Text Solution

    |

  5. Find the equation of the radical axis of the circles represented by 2x...

    Text Solution

    |

  6. Find the radical centre of the following circles. x^2 + y^2 + 4x - ...

    Text Solution

    |

  7. Show that the common chord of the circles x^2+y^2-6x-4y+9=0 and x^2+y^...

    Text Solution

    |

  8. Prove that the radical axis of the circles x^2+y^2+2gx +2fy+c=0 and x^...

    Text Solution

    |

  9. If the straight line represented by x cos alpha + y sin alpha = p inte...

    Text Solution

    |

  10. Find the equation of the circle passing through the intersection of th...

    Text Solution

    |

  11. Find the equation of the circle which cuts the circles x^2+y^2+4x+2y+1...

    Text Solution

    |

  12. If the the angle between the circles x^2+y^2-12x-6y+41=0 and x^2+y^...

    Text Solution

    |

  13. Find the equation of the circle which passes through the point (0,-3) ...

    Text Solution

    |

  14. If P and Q are conjugate points w.r.t a circle S=x^2+y^2+2gx+2fy+c=0 ,...

    Text Solution

    |

  15. If the equations of two circles whose radii are a and a' are S=0 and S...

    Text Solution

    |

  16. Find the equation of the cirlcle which cuts orthogonally the three ci...

    Text Solution

    |

  17. Find the equation of the circle passing through the intersection of th...

    Text Solution

    |

  18. If the straight line represented by x cos alpha + y sin alpha = p inte...

    Text Solution

    |

  19. Find the equations of the circles which cut orthogonally the circles ...

    Text Solution

    |

  20. Find the equation of the radical axis of the circles represented by 2x...

    Text Solution

    |