Home
Class 11
MATHS
If a!=b!=c write the condition for which...

If `a!=b!=c` write the condition for which the equations `(b-c)x+(c-a)y+(a-b)=0\ a n d\ (b^3-c^3)x+(c^3-a^3)x=y+(c^3-b^3)=0` represent the same line.

A

a+b=-c

B

c+a=-b

C

b+c=-a

D

a+b+c=0

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|34 Videos

  • STRAIGHT LINES

    OBJECTIVE RD SHARMA ENGLISH|Exercise SECTION - II (ASSERTION - REASON TYPE MCQs|1 Videos

  • SETS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

The equation (b-c)x+(c-a)y+(a-b)=0 and (b^3-c^3)x+(c^3-a^3)y+a^3-b^3=0 will represent the same line if

Prove that the lines (b-c)x+(c-a)y+(a-b)=0, (c-a)x+(a-b)y+(b-c)=0 and (a-b)x+(b-c)y+(c-a)=0 are concurrent.

To find the condition that the three straight lines A_(1)x+B_(1)y+C_(1)=0, A_(2)x+B_(2)y+C_(2)=0 and A_(3)x+B_(3)y+C_(3)=0 are concurrent.

Find the condition on a , b ,c ,d such that equations 2a x^3+bx^2+c x+d=0 and 2ax^2+3b x+4c=0 have a common root.

In a triangle A B C ,a=4,b=3,/_A=60^0 then c is root of the equation c^2-3c-7=0 (b) c^2+3c+7=0 (c) c^2-3c+7=0 (d) c^2+3c-7=0

Solve the system of the equations: a x+b y+c z=d , a^2x+b^2y+c^2z=d^2 , a^3x+b^3y+c^3z=d^3 .

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in Rdot

Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0 are equal if either b=0 or a^(3)+b^(3)+c^(3)-3acb=0

If a,b and c are the roots of the equation x^3+2x^2+1=0 , find |[a,b,c],[b,c,a],[c,a,b]| .

If a,b and c are the roots of the equation x^3+2x^2+1=0 , find |[a,b,c],[b,c,a],[c,a,b]| .

OBJECTIVE RD SHARMA ENGLISH-STRAIGHT LINES-Exercise
  1. A straight line through the point (2,2) intersects the lines sqrt(3)x+...

    Text Solution

    |

  2. Find the image of the point (3,8) with respect to the line x+3y=7 assu...

    Text Solution

    |

  3. If a!=b!=c write the condition for which the equations (b-c)x+(c-a)y+(...

    Text Solution

    |

  4. The range of theta in the interval (0,pi) such that the points (3,5) a...

    Text Solution

    |

  5. If P(sin theta, 1//sqrt(2)) and Q(1//sqrt(2), cos theta), -pi le theta...

    Text Solution

    |

  6. If the point (1, alpha) always remains in the interior of the triangle...

    Text Solution

    |

  7. Let ABC be an isosceles triangle with AB = BC. If base BC is parallel ...

    Text Solution

    |

  8. If a, c, b are in G.P then the line ax + by + c= 0

    Text Solution

    |

  9. If the intercept made on the line y=mx by lines y=2 and y=6 is less th...

    Text Solution

    |

  10. If the line 3x+4y-24=0 intersects the x-axis at the point A and the ...

    Text Solution

    |

  11. The sides of a quadrilateral are given by xy(x-2)(y-3)=0. The equatio...

    Text Solution

    |

  12. · The co-ordinates of foot of the perpendicular from the point (2, 4) ...

    Text Solution

    |

  13. Three vertices of a quadrilateral in order are (6,1)(7,2)" and "(-1,0)...

    Text Solution

    |

  14. Find the range of (alpha,2+alpha) and ((3alpha)/2,a^2) lie on the oppo...

    Text Solution

    |

  15. A point moves such that the area of the triangle formed by it with ...

    Text Solution

    |

  16. Find the coordinates of the orthocentre of the triangle whose vertices...

    Text Solution

    |

  17. If the pair of straight lines xy - x - y +1=0 & the line ax+2y-3=0 are...

    Text Solution

    |

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

    Text Solution

    |

  19. If the points (1, 2) and (3, 4) were to be on the opposite side of the...

    Text Solution

    |

  20. The coordinates of the image of the originf O with respect to the stra...

    Text Solution

    |