Home
Class 11
MATHS
If the lines ax + by + c = 0, bx + cy + ...

If the lines `ax + by + c = 0, bx + cy + a = 0` and `cx + ay + b = 0` be concurrent, then:

A

`a ^(3) + b^(3) +c^(3) +3 abc =0`

B

`a ^(3)+b^(3) +c^(3) -abc =0`

C

` a^(3) + b^(3) +c^(2) -3 abc =0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    TARGET PUBLICATION|Exercise EVALUATION TEST|10 Videos
  • STRAIGHT LINE

    TARGET PUBLICATION|Exercise CRITICAL THINKING|68 Videos
  • SETS, RELATIONS AND FUNCTIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|14 Videos
  • TRIGONOMETRIC FUNCTIONS OF COMPOUND ANGLES

    TARGET PUBLICATION|Exercise EVALUATION TEST|12 Videos

Similar Questions

Explore conceptually related problems

If the lines ax + ky + 10 =0, bx + (k+1) y + 10 =0 and cx + (k +2)y + 10=0 are concurrent, then

If the three distinct lines x + 2ay + a = 0 , x+ 3by + b = 0 and x + 4ay + a = 0 are concurrent , then the point (a,b) lies on a .

If the lines ax+by+c=0, bx+cy+a=0 and cx+ay+b=0 (a, b,c being distinct) are concurrent, then (A) a+b+c=0 (B) a+b+c=0 (C) ab+bc+ca=1 (D) ab+bc+ca=0

if a gt b gt c and the system of equations ax + by + cz = 0, bx + cy + az 0 and cx + ay + bz = 0 has a non-trivial solution, then the quadratic equation ax^(2) + bx + c =0 has

If the lines ax+by+c=0,bx+cy+a=0 and cx+ay+b=0a!=b!=c are concurrent then the point of concurrency is

If the lines (a-b-c) x + 2ay + 2a = 0 , 2bx + ( b- c - a) y + 2b = 0 and (2c+1) x + 2cy + c - a - b = 0 are concurrent , then the prove that either a+b+ c = 0 or (a+b+c)^(2) + 2a = 0

Solve: ax - by = 1 bx + ay = 0

TARGET PUBLICATION-STRAIGHT LINE -COMPETITIVE THINKING
  1. If the lines 3y+4x=1, y=x+5 and 5y+bx=3 are concurrent the n b=

    Text Solution

    |

  2. The number of values of a for which the lines 2x+y-1=0 , a x+3y-3=0, a...

    Text Solution

    |

  3. If the lines ax + by + c = 0, bx + cy + a = 0 and cx + ay + b = 0 be c...

    Text Solution

    |

  4. The lines ax + by + c = 0, where 3a + 2b + 4c= 0, are concurrent at th...

    Text Solution

    |

  5. If the lines x+ 3y -9=0 , 4x+ by -2 =0, and 2x -4 =0 are concurrent, ...

    Text Solution

    |

  6. The line passing through the point of intersection of x + y = 2,x-y = ...

    Text Solution

    |

  7. A line passes through the point of intersection of 2x +y=5 and x+ 3y+...

    Text Solution

    |

  8. The line parallel to the X-axis and passing through the point of inter...

    Text Solution

    |

  9. Find the equation of the line passing through the point of intersectio...

    Text Solution

    |

  10. Equations of line which passes through the point of intersection of th...

    Text Solution

    |

  11. A line passes through the point of intersection of the line 3x+y+1=0 a...

    Text Solution

    |

  12. 12. lf a and b are two arbitrary constants, then the straight line (a-...

    Text Solution

    |

  13. Find the distance of the point (3," "" "5) from the line 3x" "" "4y...

    Text Solution

    |

  14. Let a ne 0, b ne 0, c be three real numbers and L(p,q) =(ap + bq+c)/(...

    Text Solution

    |

  15. The length of the perpendicular drawn from orgin upon the straight lin...

    Text Solution

    |

  16. The length of the perpendicular from the origin on the line (x sin alp...

    Text Solution

    |

  17. A straight line passes through the points (5,0) and (0,3). The length ...

    Text Solution

    |

  18. If the perpendicular distance between the point(1,1) and the line 3x+4...

    Text Solution

    |

  19. What are the points on the x-axis whose perpendicular distance from th...

    Text Solution

    |

  20. Two points A and B have coordinates (1,1) and (3,-2) respectively. The...

    Text Solution

    |