Home
Class 11
MATHS
If the pairs of lines x^(2)+2xy+ay^(2)=...

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

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    CENGAGE PUBLICATION|Exercise All Questions|507 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|986 Videos

Similar Questions

Explore conceptually related problems

x^(2)dy+(x^(2)-xy+y^(2))dx=0

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

If pairs of straight lines x^2-2pxy-y^2=0 and x^2-2qxy-y^2=0 be such that each pair bisects the angle between the other pair ,then

If the radius of the circle touching the pair of lines 7x^(2) - 18 xy +7y^(2) = 0 and the circle x^(2) +y^(2) - 8x - 8y = 0 , and contained in the given circle is equal to k, then k^(2) is equal to

(x^(2) - y^(2)) dx + 2xy dy = 0

(x^(2)-2xy)dy+(x^(2)-3xy+2y^(2))dx=0

The image of the pair of lines represented by ax^(2)+2hxy+by^(2)=0 by the line mirror y=0 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.

Solve : (x^(2)-y^(2)) dx + 2xy dy = 0

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 the sum of whose intercepts on the axes is 7, is :

CENGAGE PUBLICATION-STRAIGHT LINES-All Questions
  1. The equation x^2y^2-9y^2-6x^2y+54 y=0 represents (a) a pair of stra...

    Text Solution

    |

  2. The straight lines represented by (y-mx)^(2)=a^(2)(1+m^(2))and(y-nx)^(...

    Text Solution

    |

  3. If the pairs of lines x^(2)+2xy+ay^(2)=0andax^(2)+2xy+y^(2)=0 have e...

    Text Solution

    |

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

    Text Solution

    |

  5. If the lines represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are ro...

    Text Solution

    |

  6. A point moves so that the distance between the foot of perpendicula...

    Text Solution

    |

  7. The angle between the pair of lines whose equation is 4x^(2)+10xy+my^...

    Text Solution

    |

  8. Find the point of intersection of the pair of straight lines represent...

    Text Solution

    |

  9. Find the angle between the lines represented by x^(2)+2xysectheta+y^(2...

    Text Solution

    |

  10. If the pair of lines sqrt(3)x^(2)-4xy+sqrt(3)y^(2)=0 is rotated about...

    Text Solution

    |

  11. If the equation 2x^(2)+kxy+2y^(2)=0 represents a pair of real and dist...

    Text Solution

    |

  12. If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two ...

    Text Solution

    |

  13. If one of the lines of the pair a x^2+2h x y+b y^2=0 bisects the angle...

    Text Solution

    |

  14. Prove that the equation 2x^(2)+5xy+3y^(2)+6x+7y+4=0 respresents a pai...

    Text Solution

    |

  15. A line L passing through the point (2, 1) intersects the curve 4x^2+y^...

    Text Solution

    |

  16. Show that straight lines (A^2-3B^2)x^2+8A Bx y+(B^2-3A^2)y^2=0 form wi...

    Text Solution

    |

  17. If one of the lines denoted by the line pair a x^2+2h x y+b y^2=0 bise...

    Text Solution

    |

  18. If the middle points of the sides BC, CA, and AB of triangle ABC are (...

    Text Solution

    |

  19. Find the equations of the lines which pass through the origin and are ...

    Text Solution

    |

  20. If (-2,6) is the image of the point (4,2) with respect to line L=0, th...

    Text Solution

    |