Home
Class 12
MATHS
If t(1),t(2) and t(3) are distinct, the ...

If `t_(1),t_(2) and t_(3)` are distinct, the points `(t_(1)2at_(1)+at_(1)^(3)), (t_(2),2"at"_(2)+"at_(2)^(3)) and (t_(3) ,2at_(3)+at_(3)^(3))`

A

`t_(1)t_(2)t_(3)=-1`

B

`t_(1)+t_(2)+t_(3)=t_(1)t_(2)t_(3)`

C

`t_(1)+t_(2)+t_(3)=0`

D

`t_(1)+t_(2)+t_(3)=-1`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • RECTANGULAR CARTESIAN CO-ORDINATE SYSTEM AND THE STRAIGHT LINE

    ML KHANNA|Exercise PROBLEM SET(2)(TRUE AND FALSE)|7 Videos
  • RECTANGULAR CARTESIAN CO-ORDINATE SYSTEM AND THE STRAIGHT LINE

    ML KHANNA|Exercise PROBLEM SET(2)(fill in the blanks)|2 Videos
  • RECTANGULAR CARTESIAN CO-ORDINATE SYSTEM AND THE STRAIGHT LINE

    ML KHANNA|Exercise PROBLEM SET(1)(FILL IN THE BLANK)|3 Videos
  • PROPERTIES OF TRIANGLES

    ML KHANNA|Exercise Self Assessment Test (Multiple Choise Questions)|34 Videos
  • SELF ASSESSMENT TEST

    ML KHANNA|Exercise OBJECTIVE MATHEMATICS |16 Videos

Similar Questions

Explore conceptually related problems

If t_(1)!=t_(2)!=t_(3) are the lines t_(1)x+y=2at_(1)+at_(1)^(3),t_(2)x+y=2at_(2)+at_(2)^(3),t_(3)x+y=2at_(3)+at_(3)^(3) are concurrent then t_(1)+t_(2)+t_(3)=

The points (at_(1)^(2),2at_(1)),(at_(2)^(2),2at_(2)) and (a,0) will be collinear,if

The three distinct point A(t_(1)^(2),2t_(1)),B(t_(2)^(2),2t_(2)) and C(0,1) are collinear,if

Find the area of that triangle whose vertices are (at_(1)^(2),2at_(1)),(at_(2)^(2),2at_(2))and(at_(3)^(2),2at_(3)).

If a circle intersects the parabola y^(2) = 4ax at points A(at_(1)^(2), 2at_(1)), B(at_(2)^(2), 2at_(2)), C(at_(3)^(2), 2at_(3)), D(at_(4)^(2), 2at_(4)), then t_(1) + t_(2) + t_(3) + t_(4) is

Find the are of triangle whose vertex are: (at_(1),(a)/(t_(1)))(at_(2),(a)/(t_(2)))(at_(3),(a)/(t_(3)))

Prove that the area of the triangle whose vertices are : (at_(1)^(2),2at_(1)) , (at_(2)^(2),2at_(2)) , (at_(3)^(2),2at_(3)) is a^(2)(t_(1)-t_(2))(t_(2)-t_(3))(t_(3)-t_(1)) .

Find the distance between the points (at_(1)^(2), 2 at_(1)) and (at_(2)^(2), 2 at_(2)) , where t_(1) and t_(2) are the roots of the equation x^(2)-2sqrt(3)x+2=0 and a gt 0 .

ML KHANNA-RECTANGULAR CARTESIAN CO-ORDINATE SYSTEM AND THE STRAIGHT LINE-PROBLEM SET(2)(MULTIPLE CHOICE QUESTIONS)
  1. For what value of k are the points (k ,2-2k)(-k+1,2k)a n d(-4-k ,6,6-2...

    Text Solution

    |

  2. The points (x,2x),(2y,y) and (3,3) are collinear

    Text Solution

    |

  3. If t(1),t(2) and t(3) are distinct, the points (t(1)2at(1)+at(1)^(3)),...

    Text Solution

    |

  4. The equations (b-c)x+(c-a)y+(a-b)=0 and (b^(3)-c^(3))x+(c^(3)-a^(3))y+...

    Text Solution

    |

  5. A,B,C are the points (a,p),( b,q) and (c,r) respectively such that a,b...

    Text Solution

    |

  6. If x(1), x(2), x(3) as well as y(1), y(2), y(3) are in GP, with the s...

    Text Solution

    |

  7. The points A(a,b+c),B(b,c+a),C(c,a+b) are

    Text Solution

    |

  8. If a,b,c are all unequal and different from 1 and the points ((t^(3))/...

    Text Solution

    |

  9. If the points (a,b),(c,d) and (a-c,b-d) are collinear, then

    Text Solution

    |

  10. If 25p^(2)+9q^(2)-r^(2)-30pq=0, then a point on the line px+qy+r=0 is

    Text Solution

    |

  11. The equation (1+2k)x+(1-k)y+k=0,k being parameter represents a family ...

    Text Solution

    |

  12. The family of straight lines x(a+b)+y(a-b)=2a where a and b are para...

    Text Solution

    |

  13. The set of lines ax+by+c=0 where 3a+2b+4c=0 are concurrent at the poin...

    Text Solution

    |

  14. If a,b,c are in A.P then the straight lines ax+by+c=0 will always pass...

    Text Solution

    |

  15. The equation of the line which passes through the point (-3,8) and cut...

    Text Solution

    |

  16. The eq. of the straight line which passes through the point (1,-2) and...

    Text Solution

    |

  17. The equations of the line the reciprocal of whose intercepts on the ax...

    Text Solution

    |

  18. A straight line meets the axes at A and B such that the centroid of De...

    Text Solution

    |

  19. IF the co ordinates of the mid points D,E,F of the sides BC,CA,AB of a...

    Text Solution

    |

  20. If each of the points A(x(1),4),B(-2,y(1)) lies on the line joining th...

    Text Solution

    |