Home
Class 11
MATHS
Two pairs of straight lines have the equ...

Two pairs of straight lines have the equations `y^(2)+xy-12x^(2)=0andax^(2)+2hxy+by^(2)=0`. One line will be common among them if

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    CENGAGE ENGLISH|Exercise All Questions|508 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|983 Videos

Similar Questions

Explore conceptually related problems

If the pair of lines x^(2)+2xy+ay^(2)=0 and ax^(2)+2xy+y^(2)=0 have exactly one line in common, then a =

The condition that one of the straight lines given by the equation ax^(2)+2hxy+by^(2)=0 may coincide with one of those given by the equation a'x^(2)+2h'xy+b'y^(2)=0 is

If the pairs of lines x^(2)+2xy+ay^(2)=0andax^(2)+2xy+y^(2)=0 have exactly one line in common then the joint equation of the other two lines is given by

The equation of the lines parallel to the line common to the pair of lines given by 6x^(2)-xy-12y^(2)=0 and 15x^(2)+14xy-8y^(2)=0 and the sum of whose intercepts on the axes is 7, is

The equations of a line which is parallel to the line common to the pair of lines given by 6x^(2)-xy-12y^(2)=0and15x^(2)+14xy-8y^(2)=0 and at a distance of 7 units from it is :

The angle between the straight lines given by the joint equation x^2+4xy+y^2+2x+4y+1 =0

Consider the equation of a pair of straight lines as 2x^(2)-10xy+12y^(2)+5x-16y-3=0 . The angles between the lines is theta . Then the value of tan theta is

Show that the pairs of straight lines 2x^2+6x y+y^2=0 and 4x^2+18 x y+y^2=0 have the same set of angular bisector.

Show that the pairs of straight lines 2x^2+6x y+y^2=0 and 4x^2+18 x y+y^2=0 have the same set of angular bisector.

Statement I. if alpha beta=-1 then the pair of straight lines x^2-2alphaxy-y^2=0 and y^2+2betaxy-x^2=0 are the angle bisector of each other. Statement II. Pair of angle bisector lines of the pair of lines ax^2+2hxy+by^2=0 is h (x^2-y^2)=(a-b)xy.

CENGAGE ENGLISH-STRAIGHT LINES-All Questions
  1. If the gradient one of the lines x^2+h x y+2y^2=0 is twice that of the...

    Text Solution

    |

  2. If one of the lines of my^(2)+(1-m^(2))xy-mx^(2)=0 is a bisector of th...

    Text Solution

    |

  3. Two pairs of straight lines have the equations y^(2)+xy-12x^(2)=0andax...

    Text Solution

    |

  4. If the equation of the pair of straight lines passing through the poin...

    Text Solution

    |

  5. If one of the lines given by the equation 2x^(2)+pxy+3y^(2)=0 coincide...

    Text Solution

    |

  6. If x^2+2h x y+y^2=0 represents the equation of the straight lines thro...

    Text Solution

    |

  7. The equation to a pair of opposite sides of a parallelogram are x^2-5x...

    Text Solution

    |

  8. The equation a^2x^2+2h(a+b)x y+b^2y^2=0 and a x^2+2h x y+b y^2=0 repre...

    Text Solution

    |

  9. The equation x^3+x^2y-x y^2 =y^3 represents (a)three real straight lin...

    Text Solution

    |

  10. The image of the pair of lines represented by a x^2+2h x y+b y^2=0 by ...

    Text Solution

    |

  11. The combined equation of the lines l1a n dl2 is 2x^2+6x y+y^2=0 and ...

    Text Solution

    |

  12. If the equation a x^2-6x y+y^2=0 represents a pair of lines whose slo...

    Text Solution

    |

  13. The equation of a line which is parallel to the line common to the pai...

    Text Solution

    |

  14. If the sum of the slopes of the lines given by x^2-2c x y-7y^2=0 is fo...

    Text Solution

    |

  15. Area of the triangle formed by the line x+y=3 and angle bisectors o...

    Text Solution

    |

  16. The equation x^2y^2-9y^2-6x^2y+54 y=0 represents (a)a pair of strai...

    Text Solution

    |

  17. The straight lines represented by (y-m x)^2=a^2(1+m^2) and (y-n x)^2=a...

    Text Solution

    |

  18. If the pairs of lines x^2+2x y+a y^2=0 and a x^2+2x y+y^2=0 have exact...

    Text Solution

    |

  19. The condition that one of the straight lines given by the equation a x...

    Text Solution

    |

  20. If the represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are rotated ...

    Text Solution

    |