Home
Class 12
MATHS
If the lines (a-b-c) x + 2ay + 2a = 0 , ...

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
prove that either `a+b+ c = 0 or (a+b+c)^(2) + 2a = 0 `

Promotional Banner

Topper's Solved these Questions

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 4|15 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 5|16 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 2|18 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

Similar Questions

Explore conceptually related problems

If the straight lines a x + m ay + 1 =0 b x + ( m +1) by + 1 =0 cx + (m+2) cy +1 =0, m ne0 are concurrent, then a, b, c are in :

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

If a^2 (b+c),b^2(c+a) , c^2(a+b) are in A.P., show that : either a, b, c are in A.P. or ab + bc + ca =0.

Given x = cy+bz, y = az + cx, z = b x + ay where, x,y,z are not all zero prove that a^2+b^2 +c^2 + 2 a b c = 1.

If the lines : x+2ay+a=0, x+3by+b=0 and x+4cy+c=0 are concurrent, where a,b,c are non-zero real numbers, then :

If the lines ax+by+c=0, bx+cy+a=0 and cx+ay+b=0 (a, b,c being distinct) are concurrent, then

If the straight lines x+y-2=0,2x-y+1=0 and a x+b y-c=0 are concurrent, then the family of lines 2a x+3b y+c=0(a , b , c are nonzero) is concurrent at (a) (2,3) (b) (1/2,1/3) (c) (-1/6,-5/9) (d) (2/3,-7/5)

If a, b, c are real and a!=b , then the roots ofthe equation, 2(a-b)x^2-11(a + b + c) x-3(a-b) = 0 are :

ARIHANT MATHS-THE STRAIGHT LINES-Exercise For Session 3
  1. Locus of the point of intersection of lines x cosalpha + y sin alpha =...

    Text Solution

    |

  2. If a ,\ b , c are in A.P., then the line a x+b y+c=0 passes through a ...

    Text Solution

    |

  3. If the lines a x+12 y+1=0,\ b x+13 y+1=0 and c x+14 y+1=0 are concurre...

    Text Solution

    |

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

    Text Solution

    |

  5. If the lines ax+y+1=0, x+by+1=0 and x+y+c=0 (a,b and c being distinct ...

    Text Solution

    |

  6. If u=a1x+b1y+c1=0,v=a2x+b2y+c2=0, and (a1)/(a2)=(b1)/(b2)=(c1)/(c2), t...

    Text Solution

    |

  7. The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent...

    Text Solution

    |

  8. If the straight lines x+y-2=0,2x-y+1=0 and a x+b y-c=0 are concurrent,...

    Text Solution

    |

  9. The straight line through the point of intersection of ax + by+c=0 and...

    Text Solution

    |

  10. If the equations of three sides of a triangle are x+y=1, 3x + 5y = 2 a...

    Text Solution

    |

  11. Find the equations of the line through the intersection of 2x - 3y + 4...

    Text Solution

    |

  12. The locus of point of intersection of the lines x/a-y/b=m and x/a+y/b...

    Text Solution

    |

  13. The condition on a and b , such that the portion of the line a x+b y-1...

    Text Solution

    |

  14. If the lines (a-b-c) x + 2ay + 2a = 0 , 2bx + ( b- c - a) y + 2b = 0 ...

    Text Solution

    |

  15. If the lines ax+by+c=0, bx+cy+a=0 and cx+ay+b=0 (a, b,c being distinct...

    Text Solution

    |

  16. Find the equation of the straight line which passes through the inte...

    Text Solution

    |

  17. Let a ,\ b ,\ c be parameters. Then the equation a x+b y+c=0 will repr...

    Text Solution

    |

  18. Prove that the family of lines represented by x(1+lambda)+y(2-lambda)+...

    Text Solution

    |

  19. Prove that (-a,-a/2) is the orthocentre of the triangle formed by the ...

    Text Solution

    |