Home
Class 12
MATHS
The abscissae of the two points A and B ...

The abscissae of the two points A and B are the roots of the equation `x^(2) + 2ax-b^(2) =0` and their ordinates are the roots of the equation `x^(2)+2px-q^(2)=0`. Find the equation and the radius of the circle with `bar(AB)` as diameter.

Text Solution

Verified by Experts

The correct Answer is:
`x^(2) + y^(2) + 2ax + 2py - b^(2) - q^(2) = 0, sqrt(a^(2) + b^(2) + p^(2) + q^(2))` unit
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 abscissae of two points A and B are the roots of the equation x^2+2ax-b^2=0 and their ordinates are the equation x^2+2px-q^2=0 .Find the equation and the radis of the circle with AB as diameter.

If , p , q are the roots of the equation x^(2)+px+q=0 , then

If p and q are the roots of the equation x^2+px+q =0, then

Find the roots of the equation 2x^2 - x + 1/8 = 0

IF the equation 4x^2+2bx+c=0,b=0 , find the relation between the roots of the equation.

If alpha and beta are the roots of the equation ax^(2)+bx+c=0 then the sum of the roots of the equation a^(2)x^(2)+(b^(2)-2ac)x+b^(2)-4ac=0 is

If the ratio of the roots of the equation x^2-px+q=0 be 1:2 , find the relation between p and q.

If p,q are odd integers, then the roots of the equation 2px^(2)+(2p+q)x+q=0 are

Find the root of equation 2x^2+3 x + 11=0.

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

    |