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 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

  • CIRCLE

    CENGAGE ENGLISH|Exercise Multiple Correct Anser Type|29 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise Linked Comprehension Type (For Problem 1-3)|3 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 4.20|1 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Matrix|4 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

Similar Questions

Explore conceptually related problems

Show that the distance of the centre of the circle x^2+y^2=2x from the common chord of the circles x^2+y^2+5x-8y+1=0 and x^2+y^2-3x+7y-25=0 is 2.

Common chord of the circles x^2+y^2-4x-6y+9=0, x^2+y^2-6x-4y+4=0 is

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

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

The distance of the point (1, 2) from the common chord of the circles x^2+y^2-2x+3y-5=0 and x^2+y^2+10x+8y=1 is

The distance of the point (1,-2) from the common chord of the circles x^(2) + y^(2) - 5x +4y - 2= 0 " and " x^(2) +y^(2) - 2x + 8y + 3 = 0

The equation of the circle described on the common chord of the circles x^2 +y^2- 4x +5=0 and x^2 + y^2 + 8y + 7 = 0 as a diameter, is

The point of tangency of the circles x^2+ y^2 - 2x-4y = 0 and x^2 + y^2-8y -4 = 0 , is

The point of tangency of the circles x^2+ y^2 - 2x-4y = 0 and x^2 + y^2-8y -4 = 0 , is

CENGAGE ENGLISH-CIRCLE -Excercises (Single Correct Answer Type)
  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 centre of the circle which cut the circles x^2+y...

    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=2 is the equation of a transverse common tangent...

    Text Solution

    |

  15. Let C1 and C2 are circles defined by x^2+y^2 -20x+64=0 and x^2+y^2+...

    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 the centre of the circle which touches x^2+y^2 - 6x-6y+14 =0 ...

    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

    |