Home
Class 11
MATHS
Statement 1 : If two circles x^2+y^2+2gx...

Statement 1 : If two circles `x^2+y^2+2gx+2fy=0` and `x^2+y^2+2g^(prime)x+2f^(prime)y=0` touch each other, then `f^(prime)g=fg^(prime)dot` Statement 2 : Two circles touch other if the line joining their centers is perpendicular to all possible common tangents.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

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

If two circle x^(2)+y^(2)+2gx +2fy=0 and x^(2)+y^(2)+2g'x+2f'y=0 touch each other then proove that f'g =fg'.

If circles x^(2) + y^(2) + 2g_(1)x + 2f_(1)y = 0 and x^(2) + y^(2) + 2g_(2)x + 2f_(2)y = 0 touch each other, then

If two circles and a(x^2 +y^2)+bx + cy =0 and p(x^2+y^2)+qx+ry= 0 touch each other, then

The circles x^(2)+y^(2)+2x-2y+1=0 and x^(2)+y^(2)-2x-2y+1=0 touch each other

Prove that the circle x^(2)+y^(2)+2x+2y+1=0 and circle x^(2)+y^(2)-4x-6y-3=0 touch each other.

Examine whether the two circles x^2+y^2-2x-4y=0 and x^2+y^2-8y-4=0 touch each other externally or internally .

Two circles x^2 + y^2 + 2x-4y=0 and x^2 + y^2 - 8y - 4 = 0 (A) touch each other externally (B) intersect each other (C) touch each other internally (D) none of these

If the two circles x^(2)+y^(2)+2gx+c=0 and x^(2)+y^(2)-2fy-c=0 have equal radius then locus of (g,f) is

Circles x^(2) + y^(2) - 2x = 0 and x^(2) + y^(2) + 6x - 6y + 2 = 0 touch each other extermally. Then point of contact is

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Statement 1 : The equation of chord through the point (-2,4) which is ...

    Text Solution

    |

  2. intdx/(x(x^5 + 1))

    Text Solution

    |

  3. Statement 1 : If two circles x^2+y^2+2gx+2fy=0 and x^2+y^2+2g^(prime)x...

    Text Solution

    |

  4. Find the greatest distance of the point P(10 ,7) from the circle x^2+y...

    Text Solution

    |

  5. Statement 1 : If the circle with center P(t ,4-2t),t in R , cut the c...

    Text Solution

    |

  6. Find the area of the region in which the points satisfy the inequaties...

    Text Solution

    |

  7. If points A and B are (1, 0) and (0, 1), respectively, and point C is ...

    Text Solution

    |

  8. If the line x+2b y+7=0 is a diameter of the circle x^2+y^2-6x+2y=0 , t...

    Text Solution

    |

  9. Column I|Column II If the circle lies in the first quadrant, the...

    Text Solution

    |

  10. Find the number of point (x ,y) having integral coordinates satisfying...

    Text Solution

    |

  11. The circle x^2+y^2-6x-10 y+k=0 does not touch or intersect the coordin...

    Text Solution

    |

  12. Statement 1 :The circles x^2+y^2+2p x+r=0 and x^2+y^2+2q y+r=0 touch i...

    Text Solution

    |

  13. If the circle x^2+y^2+2x+3y+1=0 cuts x^2+y^2+4x+3y+2=0 at A and B , th...

    Text Solution

    |

  14. If the radii of the circles (x-1)^2+(y-2)^2+(y-2)^2=1 and (-7)^2+(y-10...

    Text Solution

    |

  15. Aa n dB are two points in the xy-plane, which are 2sqrt(2) units dista...

    Text Solution

    |

  16. Two circles with radii a and b touch each other externally such that t...

    Text Solution

    |

  17. From the variable point A on circle x^2+y^2=2a^2, two tangents are dra...

    Text Solution

    |

  18. Two fixed circles with radii r1 and r2,(r1> r2) , respectively, touch ...

    Text Solution

    |

  19. If the circle x^2+y^2+2gx+2fy+c=0 is touched by y=x at P such that O P...

    Text Solution

    |

  20. Find the radius of the smallest circle which touches the straight line...

    Text Solution

    |