Home
Class 12
MATHS
If the two straight lines 3x - 2y = 8 an...

If the two straight lines 3x - 2y = 8 and 2x - y = 5 lie along two diameters of a circle, which touches the x-axis, find the equation of the circle.

Text Solution

Verified by Experts

The correct Answer is:
`x^(2) + y^(2) - 4x + 2y + 4 = 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

3x+y=5 and x+y-1=0 are the equations of two diamters to the circle,which passes through the point (-2,2).Find the equation of the circle.

Find the equations of circles which touch the axes and whose centres lie on the line x-2y=3

The equation of two diameters of a circle of area 154 sq unit are 2x-3y=5 and 3x-4y=7 . Find the equation of the circle.

If the lines 2x-3y-5=0 and 3x-4y=7 are diameters of a circle of area 154 sq. units, then the equation of the circle is

If the lines x+y=6 and x+2y=4 are diameters of the circle which passes through the point (2, 6), then find its equation.

A circle has its centre on the straight line 5x - 2y + 1 = 0 and cuts the x-axis at the two points whose abscissae are (-5) and 3, find the equation of the circle and its radius.

3x + y = 5 and x+y+1 = 0 are two diameters to the circle which passes through the point (-2, 2). Find its equation. Also find the radius of the circle.

If a circle is concentric with the circle x^(2) + y^(2) = 8 and its diameter is 4 units , which of the following will be the equation of the circle ?

Find the equations of the circle which touches y-aixs at (0,5) and whose centre lies on the line 2x+y=13.

The equations of two diameters of a circle are x-2y+1 = 0 and x+y -2 = 0 and the length of the chord intercepted on the straight line 3x + 4y + 8 = 0 by the circle is 6 units. Find the equation of the circle.

CHHAYA PUBLICATION-CIRCLE-Exercise 3 (Long Answer Type Questions)
  1. Find the equations to the circles which touch the y-axis and pass thro...

    Text Solution

    |

  2. If the two straight lines 3x - 2y = 8 and 2x - y = 5 lie along two dia...

    Text Solution

    |

  3. A circle touches the lines x = 0 , y = 0 and x + y = 1. If the centre ...

    Text Solution

    |

  4. Find the equations to the circles which touch the axis of y at a dista...

    Text Solution

    |

  5. A circle passes through the point (-2, 1) and touches the straight lin...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |