Home
Class 12
MATHS
The circles ax^(2)+ay^(2)+2g(1)x+2f(1)y+...

The circles `ax^(2)+ay^(2)+2g_(1)x+2f_(1)y+c_(1)=0` and `bx^(2)+by^(2)+2g_(2)x+2f_(2)y+c_(2)=0` (`a ne 0` and `b ne 0`) cut orthogonally if

A

g_(1)g_{2)+f_(1)f_{2) = bc_(1)+ac_(1)

B

g_(1)g_{2)+f_(1)f_{2) = ac_(1)+bc_(2)

C

g_(1)g_{2)+f_(1)f_{2) = c_(1)+c_(2)

D

2g_(1)g_{2)+2f_(1)f_{2) = bc_(1)+ac_(2)

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|200 Videos

  • COMMON ENTRANCE TEST - 2014

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|60 Videos

Similar Questions

Explore conceptually related problems

The locus of the centre of the circle which cuts the circles x^(2)+y^(2)+2 g_(1) x+2 f_(1) y+c_(1)=0 x^(2)+y^(2)+2 g_(2) x+2 f_(2) y+c_(2)=0 orthogonally is

The circleS x^(2)+y^(2)+2 a x+c^2=0 and x^(2)+y^(2)+2 b y+c^2=0 touch if

If the circles x^(2)+y^(2)+2gx+2fy=0 and x^(2)+y^(2)+2g'x+2f'y=0 touch each other, then

In the pair of linear equations a_(1)x +b_(1)y +c_(1)=0 and a_(2)x +b_(2)y +c_(2)=0 if (a_(1))/(a_(2)) ne (b_(1))/(b_(2)) then the

For the circles x^(2) + y^(2) - 2x + 3y + k = 0 and x^(2) + y^(2) + 8x - 6y - 7 = 0 to cut each other orthogonally the value of k must be

If the radical axis of the circles x^(2)+y^(2)+2gx + 2fy + c = 0 and 2x^(2) + 2y^(2) + 3x + 8y + 2c =0 touches the circle x^(2)+ y^(2)+2x+2y + 1 = 0, then

Prove that the circle x^(2) + y^(2) + 2ax + c^(2) = 0 and x^(2) + y^(2) + 2by + c^(2) = 0 touch each other if (1)/(a^(2)) + (1)/(b^(2)) = (1)/(c^(2)) .

Show that two lines a_(1)x + b_(1) y+ c_(1) = 0 " and " a_(2)x + b_(2) y + c_(2) = 0 " where " b_(1) , b_(2) ne 0 are : (i) Parallel if a_(1)/b_(1) = a_(2)/b_(2) , and (ii) Perpendicular if a_(1) a_(2) + b_(1) b_(2) = 0 .

If P=(x, y), F_(1)=(3,0), F_(2)=(-3,0) and 16 x^(2)+25 y^(2)=400 then P F_(1)+P F_(2)=

HIMALAYA PUBLICATION-CIRCLES-QUESTION BANK
  1. The two circles x^(2) + y^(2) - 2x + 22y + 5 = 0 and x^(2) + y^(2) + 1...

    Text Solution

    |

  2. If the length of the tangent from any point on the circle (x-3)^(2)+(y...

    Text Solution

    |

  3. The circles ax^(2)+ay^(2)+2g(1)x+2f(1)y+c(1)=0 and bx^(2)+by^(2)+2g(2)...

    Text Solution

    |

  4. The equation of the common tangent of the two touching circles, y^(2)+...

    Text Solution

    |

  5. If the line 2 x+3 y+k=0 is a tangtnt to the circle x^(2)+y^(2)-6 x-8 ...

    Text Solution

    |

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

    Text Solution

    |

  7. x^(2) + y^(2) -6x -6y + 4 = 0, x^(2) + y^(2) -2x -4y + 3 = 0, x^(2) + ...

    Text Solution

    |

  8. If the circles x^(2)+y^(2)-2 x-2 y-7=0 and x^(2)+y^(2)+4 x+2 y+k=0 cu...

    Text Solution

    |

  9. If two circleS x^(2)+y^(2)+2 lambda x+c=0 and x^(2)+y^(2)-2 mu y-c=0 ...

    Text Solution

    |

  10. Given that the circle x^(2)+y^(2)+2 x-4 y+4=0 and x^(2)+y^(2)-2 x-4 y...

    Text Solution

    |

  11. The equation ot the circle concentric with x^(2)+y^(2)+6 x+2 y+1=0 an...

    Text Solution

    |

  12. The centre of a circle passing through the points (0,0),(1,0) and tou...

    Text Solution

    |

  13. The equation of the tangent to the circle x^2 + y^2 + 4x - 4y + 4 = 0 ...

    Text Solution

    |

  14. The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having...

    Text Solution

    |

  15. If a circle passes through the point (a, b) and cuts x^2+y^2=4 orthogo...

    Text Solution

    |

  16. Locus of centroid of the triangle whose vertices are (a cos t, a sin ...

    Text Solution

    |

  17. If two circle (x-1)^(2)+(y-3)^(2)=r^(2) and x^(2)+y^(2)-8x+2y+8=0 inte...

    Text Solution

    |

  18. A variable circle passes through the fixed point A (p, q) and touches ...

    Text Solution

    |

  19. If the lines 2x+3y+1=0 and 3x-y-4=0 lie along diameters of a circle of...

    Text Solution

    |

  20. The intercept on the line y = x by the circle x^2+y^2-2x=0 is AB. Equ...

    Text Solution

    |