Home
Class 11
MATHS
If the equation x^2+(lambda+mu)x y+lambd...

If the equation `x^2+(lambda+mu)x y+lambdau y^2+x+muy=0` represents two parallel straight lines, then prove that `lambda=mu`.

A

`lambda | mu=0`

B

`lambda=4mu`

C

`lambda-mu`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
The given equation will represent a pair of parallel lines, if
`((lambda+mu)/(2))^(2)=lambdamu" "["Using ":h^(2)=ab]`
`rArr" "(lambda-mu)^(2)rArr lambda=mu`
Promotional Banner

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA ENGLISH|Exercise SOLVED MCQs|1 Videos

  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|3 Videos

  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|28 Videos

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

If the equation (4 lambda - 3) x^(2) + lambda y ^(2) + 6x - 2y + 2 = 0 represents a circle, then its centre is

The equation (x^(2))/(10-lambda)+(y^(2))/(6-lambda)=1 represents

The equation (x^2)/(12-lambda)+(y^2)/(8-lambda)=1 represents

If the equation x^(2)+y^(2)+6x-2y+(lambda^(2)+3lambda+12)=0 represent a circle. Then

If lambdax^(2)-10xy+12y^(2)+5x-16y-3=0 , represents a pair of straight lines, then the value of lambda is

Find the value of lambda for which the equation lambdax^2 + 4xy + y^2 + lambdax + 3y + 2=0 represents a pair of straight line

The value of lambda for which the equation x^2-y^2 - x - lambda y - 2 = 0 represent a pair of straight line, are

Find the value of lambda if 2x^2+7x y+3y^2+8x+14 y+lambda=0 represents a pair of straight lines

Find the value of lambda if 2x^2+7x y+3y^2+8x+14 y+lambda=0 represents a pair of straight lines

The equation (x^2)/(2-lambda)+(y^2)/(lambda-5)+1=0 represents an elipse, if

OBJECTIVE RD SHARMA ENGLISH-PAIR OF STRAIGHT LINES-Section I - Solved Mcqs
  1. If one of the lines of the pair a x^2+2h x y+b y^2=0 bisects the angle...

    Text Solution

    |

  2. The equation kx^2+4xy+5y^2=0 represents two lines inclined at an angle...

    Text Solution

    |

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

    Text Solution

    |

  4. If the gradient one of the lines ax^2+2h x y+by^2=0 is twice that of t...

    Text Solution

    |

  5. The equation x^(3)+y^(3)=0 represents

    Text Solution

    |

  6. One bisector of the angle between the lines given by a(x-1)^(2)+2h(x-1...

    Text Solution

    |

  7. The equation 2x^(2)-3xy-py^(2)+x+qy-1=0 represent two mutually perpend...

    Text Solution

    |

  8. The product of the perpendiculars drawn from the point (1,2) to the pa...

    Text Solution

    |

  9. The three lines whose combined equation is y^(3)-4x^(2)y=0 form a tria...

    Text Solution

    |

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

    Text Solution

    |

  11. Show that the condition that two of the three lines represented by ax^...

    Text Solution

    |

  12. The orthocentre of the triangle formed by the pair of lines 2x^(2)-xy-...

    Text Solution

    |

  13. If the distance of a point (x(1),y(1)) from each of the two straight l...

    Text Solution

    |

  14. The equation of two straight lines through the point (x(1),y(1)) and p...

    Text Solution

    |

  15. The equation of the straigh lines through the point (x(1),y(1)) and pa...

    Text Solution

    |

  16. The triangle formed by the lines whose combined equation is (y^2 - 4xy...

    Text Solution

    |

  17. Find the combined equation of the pair of lines through the point (1, ...

    Text Solution

    |

  18. The equation x^(3)+ax^(2)y+bxy^(2)+y^(3)=0 represents three straight l...

    Text Solution

    |

  19. The combined equation of the lines L(1) and L(2) is 2x^(2)+6xy+y^(2)=0...

    Text Solution

    |

  20. The lines represented by x^(2)+2lambda xy+2y^(2)=0 and the lines repre...

    Text Solution

    |