Home
Class 12
MATHS
The distance from the center of the circ...

The distance from the center of the circle `x^2+y^2=2x` to the common chord of the circles `x^2+y^2+5x-8y+1=0` and `x^2+y^2-3x+7y-25=0` is (a)2 (b) 4 (c) `(34)/(13)` (d) `(26)/(17)`

A

2

B

4

C

`34//13`

D

`26//17`

Text Solution

Verified by Experts

The correct Answer is:
1
The center of the circle `x^(2)+y^(2)=2x` is (1,0).
The common chord of the other two circle is
`8x-15y+26=0`
The distance from (1,0) to `8x-15y+26=0` is
`(|8+26|)/(sqrt(15^(2)+8^(2)))=2`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

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 two circles x^2+y^2-4y=0 and x^2+y^2-8x-4y+11=0 is

Which of the following is a point on the common chord of the circle x^2+y^2+2x-3y+6=0 and x^2+y^2+x-8y-31=0? (a) (1,-2) (b) (1,4) (c)(1,2) (d) 1,-4)

The line x+3y=0 is a diameter of the circle x^2+y^2-6x+2y=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 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 number of common tangent to the circles x^2+y^2+2x+8y-23=0 and x^2+y^2-4x-10 y+9=0

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

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

Find the middle point of the chord of the circle x^2+y^2=25 intercepted on the line x-2y=2

CENGAGE-CIRCLE -Exercise (Single)
  1. Let A B be chord of contact of the point (5,-5) w.r.t the circle x^2+y...

    Text Solution

    |

  2. Two congruent circles with centered at (2, 3) and (5, 6) which inter...

    Text Solution

    |

  3. The distance from the center of the circle x^2+y^2=2x to the common ch...

    Text Solution

    |

  4. A circle C1, of radius 2 touches both x-axis and y- axis. Another circ...

    Text Solution

    |

  5. Suppose a x+b y+c=0 , where a ,ba n dc are in A P be normal to a famil...

    Text Solution

    |

  6. Two circles of radii aa n db touching each other externally, are inscr...

    Text Solution

    |

  7. If the length of the common chord of two circles x^2+y^2+8x+1=0 and x^...

    Text Solution

    |

  8. If r1a n dr2 are the radii of the smallest and the largest circles, re...

    Text Solution

    |

  9. If C1: x^2+y^2=(3+2sqrt(2))^2 is a circle and P A and P B are a pair o...

    Text Solution

    |

  10. P is a point (a , b) in the first quadrant. If the two circles which p...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |