Home
Class 12
MATHS
The circle x^(2) + y^(2) + 2x - 4y - 11 ...

The circle `x^(2) + y^(2) + 2x - 4y - 11 = 0` and the line `x-y+1=0` intersect at A and B. Find the equation to the circle on AB as diameter.

Text Solution

Verified by Experts

The correct Answer is:
`x^(2) + y^(2) - 2y- 13 = 0`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (MCQs)|5 Videos

  • CIRCLE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (B Integer Answer Type)|5 Videos

  • CIRCLE

    CHHAYA PUBLICATION|Exercise Exercise 3 (Short Answer Type Questions)|41 Videos

  • CALCULUS

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2014)|2 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVE EXAMS(Multiple Corrrect Answer type)|11 Videos

Similar Questions

Explore conceptually related problems

The circle x^2+y^2-8x = 0 and hyperbola x^2 /9 - y^2 /4=1 intersect at the points A and B. Then the equation of the circle with AB as its diameter is

The circle x^2 + y^2 - 2x - 4y + 1 = 0 and x^2 + y^2 + 4x + 4y - 1 = 0

The straight line x+y - 1= 0 cuts the circle x^(2) + y^(2) - 6x - 8y = 0 at A and B. Find the equation of the circle of which AB is a diameter.

If the circle x^2+y^2+2x+3y+1=0 cuts x^2+y^2+4x+3y+2=0 at A and B , then find the equation of the circle on A B as diameter.

Show that the circle x^(2) + y^(2) + 6(x-y) + 9 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x-y+4 = 0 and which also passes through the origin.

Show that the circle x^(2) + y^(2) + 4(x+y) + 4 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x+y+2 = 0 and which also passes through the origin.

The ellipse 4x^2+9y^2=36 and the hyperbola a^2x^2-y^2=4 intersect at right angles. Then the equation of the circle through the points of intersection of two conics is (a) x^2+y^2=5 (b) sqrt(5)(x^2+y^2)-3x-4y=0 (c) sqrt(5)(x^2+y^2)+3x+4y=0 (d) x^2+y^2=25

Prove that the centres of the circles x^(2) + y^(2) - 10x + 9 = 0, x^(2) + y^(2) - 6x + 2y + 1 = 0 and x^(2) + y^(2) - 18x - 4y + 21 = 0 lie on a line, find the equation of the line on which they lie.

The intercept on the line y = x by the circle x^2+y^2-2x=0 is AB. Equation of the circle with AB as diameter is

The line y = mx intersects the circle x^(2)+y^(2) -2x - 2y = 0 and x^(2)+y^(2) +6x - 8y =0 at point A and B (points being other than origin). The range of m such that origin divides AB internally is

CHHAYA PUBLICATION-CIRCLE-Exercise 3 (Long Answer Type Questions)
  1. Find the equation of the circle which touches the x-axis at a distance...

    Text Solution

    |

  2. Show that the circles x^(2) + y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(...

    Text Solution

    |

  3. Prove that the circles x^(2) + y^(2) + 4x - 10y - 20 = 0 and x^(2) + y...

    Text Solution

    |

  4. If the circles x^(2) + y^(2) + 2ax + c^(2) = 0 and x^(2) + y^(2) + 2by...

    Text Solution

    |

  5. Prove that the circles x^(2) + y^(2) - 2x - 4y - 12 = 0 and 3x^(2) + 3...

    Text Solution

    |

  6. Show that the circle x^(2) + y^(2) + 6(x-y) + 9 = 0 touches the coordi...

    Text Solution

    |

  7. A circle through the common points of the circles x^(2) + y^(2) - 2x ...

    Text Solution

    |

  8. The circle x^(2) + y^(2) + 2x - 4y - 11 = 0 and the line x-y+1=0 inter...

    Text Solution

    |

  9. Find the equation to the circle described on the common chord of the c...

    Text Solution

    |

  10. Find the equation to the locus of mid-points of chords drawn through t...

    Text Solution

    |

  11. A circle passes through the origin O and intersects the coordinate axe...

    Text Solution

    |

  12. Find the equation of a circle circumscribing the triangle whose sides ...

    Text Solution

    |

  13. Find the area of the equilateral triangle inscribed in the circle x^(2...

    Text Solution

    |

  14. Find the area of the equilateral triangle inscribed in the circle x^(2...

    Text Solution

    |

  15. Prove analytically that the straight line joining the middle point of ...

    Text Solution

    |

  16. Find the equation of the circle passing through the point (13, 6) and ...

    Text Solution

    |

  17. Show that the length of the common chord of the circles (x-a)^(2) + (y...

    Text Solution

    |

  18. The abscissae of the two points A and B are the roots of the equation ...

    Text Solution

    |

  19. Find the equation of the circle which touches the x-axis at a distance...

    Text Solution

    |

  20. Prove that the circles x^(2) + y^(2) + 4x - 10y - 20 = 0 and x^(2) + y...

    Text Solution

    |