Home
Class 11
MATHS
If the lines x-2y-6=0, 3x+y -4=0 and lam...

If the lines x-2y-6=0, 3x+y -4=0 and `lambdax+4y+lambda^2=0` and concurrent, and it is given that `lambda inR^+, lambda`=

Text Solution

Verified by Experts

`|[1,-2,-6],[3,1,-4],[lambda,4,lambda^2]|=0implieslambda^2+2lambda-8=0`
`implies(lambda+4)(lambda-2)=0` `therefore lambda inR^+`, so `lambda=2`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

Similar Questions

Explore conceptually related problems

Prove that the lines 2x-3y-7=0,3x-4y-13=0 and 8x-11y-33=0 are concurrent.

If the lines 3x^(2)-4xy +y^(2) +8x - 2y- 3 = 0 and 2x - 3y +lambda = 0 are concurrent, then the value of lambda is

If the lines 2x + y - 3 = 0 , 5x + ky - 3 = 0 " and " 3x - y - 2 = 0 are concurrent , find the value of k.

The lines 2x-y-1=0, ax+3y-3=0 and 3x+2y-2=0 are concurrent for

If the straight lines x+q=0 , y-2 =0 and 3x+ 2y+5=0 are concurrent, then the value of q is-

If the equation 4x^2-x-1=0 and 3x^2+(lambda+mu)x+lambda-mu=0 have a root common, then the irrational values of lambda and mu are a lambda=(-3)/4 b. lambda=0 c. mu=3/4 b. mu=0

Examine whether the striaght lines x-y+4=0,2x+3y-6=0 and 8x+7y-26=0 are concurrent or not.

If the equation |x^2-5x + 6|-lambda x+7 lambda=0 has exactly 3 distinct solutions then lambda is equal to

If a circle passes through the point of intersection of the lines x+ y +1=0 and x+ lambda y-3=0 with the coordinate axis, then find the value of lambda .

If x^2-3xy+lambda y^2+3x-5y+2=0 ,represent a pair of straight lines, then the value of lambda is

PATHFINDER-CARTESIAN COORDINATES AND STRAIGHT LINE-QUESTION BANK
  1. Match the List I with List II and select the correct option.

    Text Solution

    |

  2. If the lines ax+by+c=0, bx+cy+a=0 and Cx+ay+b=0 are concurrent (a+b+cn...

    Text Solution

    |

  3. If the lines x-2y-6=0, 3x+y -4=0 and lambdax+4y+lambda^2=0 and concurr...

    Text Solution

    |

  4. Let, ax+by+c=0 be a variable straight line, where, a, b, c are 1^(st),...

    Text Solution

    |

  5. The length of the largest altitude of triangle formed by the straight ...

    Text Solution

    |

  6. The area of the triangle formed by the axes and the line e^(-alpha)x+e...

    Text Solution

    |

  7. The only integral value of alpha, such that the point P(alpha,2) lines...

    Text Solution

    |

  8. The vertices of a triangle are [at1t2, a(t1+t2)],[at2t3,a(t2+t3)],[at...

    Text Solution

    |

  9. One diagonal of a square is the intercept of the line x/a+y/b=1 betwee...

    Text Solution

    |

  10. Find alpha if (alpha, alpha^2) lies inside the triangle having sides a...

    Text Solution

    |

  11. If the lines ax+y+1=0, x+by+1=0, x+y+c=0, (a, b, c are distinct and no...

    Text Solution

    |

  12. Prove that all lines represented by the equation (2costheta+3sintheta)...

    Text Solution

    |

  13. A line through A(-5,-4) meets the lines x+3y+2=0, 2x+y+4=0 and x-y-5=0...

    Text Solution

    |

  14. Given n straight line and a fixed point O, a straight line is drawn th...

    Text Solution

    |

  15. Find the condition that two of the three lines represented by ax^3+bx^...

    Text Solution

    |

  16. If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of para...

    Text Solution

    |

  17. If the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 represents a pa...

    Text Solution

    |

  18. prove that the product of the perpendiculars drawn from the point (x1,...

    Text Solution

    |

  19. The orthocentre of a triangle whose vertices are (0,0),(sqrt3,0) and (...

    Text Solution

    |

  20. The image of the point (3,8) with respect to the line x+3y=7 is

    Text Solution

    |