Home
Class 12
MATHS
Prove that the length of the common chor...

Prove that the length of the common chord of the two circles :
`(x-a)^(2)+(y-b)^(2)=c^(2)and(x-b)^(2)+(y-a)^(2)=c^(2)" is "sqrt(4c^(2)-2(a-b)^(2))`
Find also the condition when the given circles touch.

A

`a = b+- 2c`

B

`a= b+- sqrt(2) c `

C

`a= b+-c `

D

`a= b^(2) -c`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    VMC MODULES ENGLISH|Exercise LEVEL-2|50 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise NUMERICAL VALUE TYPE FOR JEE MAIN|15 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise JEE Archive|56 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

The length of the common chord of the circles (x-a)^(2)+(y-b)^(2)=c^(2) and (x-b)^(2)+(y-a)^(2)=c^(2) , is

The length of the common chord of the circles (x-6)^2+(y-4)^2=4, (x-4)^2+(y-6)^2=4 is

The equation of the circle on the common chord of the circles (x-a)^(2)+y^(2)=a^(2) and x^(2)+(y-b)^(2)=b^(2) as diameter, is

The length of the common chord of the circles x^(2)+y^(2)-2x-1=0 and x^(2)+y^(2)+4y-1=0 , is

If the circles (x-a)^(2)+(y-b)^(2)=c^(2) and (x-b)^(2)+(y-a)^(2)=c^(2) touch each other, then

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

The length of the common chord of the circles x^2+y^2+ax+by+c=0 and x^2+y^2+bx+ay+c=0 is

Find the length of the common chord of the parabola y^2=4(x+3) and the circle x^2+y^2+4x=0 .

Find the length of the common chord of the parabola y^2=4(x+3) and the circle x^2+y^2+4x=0 .

The length of the common chord of the ellipse ((x-1)^2)/9+((y-2)^2)/4=1 and the circle (x-1)^2+(y-2)^2=1 is (A) 2 (B) sqrt3 (C) 4 (D) none of these

VMC MODULES ENGLISH-CIRCLES-LEVEL-1
  1. The locus of the centre of the circles which touches both the axes is ...

    Text Solution

    |

  2. The circumcentre of the triangle formed by the lines, xy + 2x + 2y + 4...

    Text Solution

    |

  3. The locus of the midpoint of a chord of the circle x^2+y^2=4 which sub...

    Text Solution

    |

  4. The line ax+by+by+c=0 is normal to the circle x^(2)+y^(2)+2gx+2fy+d=0...

    Text Solution

    |

  5. If the points (2, 0), (0, 1), (4, 5)and (0, c) are concyclic, then th...

    Text Solution

    |

  6. If a circle of constant radius 3k passes through the origin O and meet...

    Text Solution

    |

  7. Find the equation of the circle passing through (1,0)a n d(0,1) and ha...

    Text Solution

    |

  8. The equation of the circle which touches the axes of coordinates an...

    Text Solution

    |

  9. The circle x^(2)+y^(2)+4x-7y+12=0 cuts an intercept on Y-axis is of le...

    Text Solution

    |

  10. The shortest distance from the point (2,-7) to thwe circe x^(2)+y^(2)-...

    Text Solution

    |

  11. Find the number of integral values of lambda for which x^2+y^2+lambdax...

    Text Solution

    |

  12. Prove that the length of the common chord of the two circles : (x-a)...

    Text Solution

    |

  13. Find the number of common tangents that can be drawn to the circles...

    Text Solution

    |

  14. Show that the circles x^(2) + y^(2) + 2 x -6 y + 9 = 0 and x^(2) +y^(2...

    Text Solution

    |

  15. If two circles (x-1)^(2)+(y-3)^(2)=r^(2) and x^(2)+y^(2)-8x+2y+8=0 int...

    Text Solution

    |

  16. The abscissa of the two points A and B are the roots of the equation x...

    Text Solution

    |

  17. If circles x^(2) + y^(2) + 2g(1)x + 2f(1)y = 0 and x^(2) + y^(2) ...

    Text Solution

    |

  18. Two vertices of an equilateral triangle are (-1,0) and (1, 0), and its...

    Text Solution

    |

  19. If the line y = mx - (m-1) cuts the circle x^2+y^2=4 at two real and d...

    Text Solution

    |

  20. The length of the chord of the circle x^(2)+y^(2)=9 passing through (...

    Text Solution

    |