Home
Class 12
MATHS
Three sided of a triangle have equations...

Three sided of a triangle have equations `L_1-=y-m_i x=o; i=1,2a n d3.` Then `L_1L_2+lambdaL_2L_3+muL_3L_1=0` where `lambda!=0,mu!=0,` is the equation of the circumcircle of the triangle if `1+lambda+mu=m_1m_2+lambdam_2m_3+lambdam_3m_1` `m_1(1+mu)+m_2(1+lambda)+m_3(mu+lambda)=0` `1/(m_3)+1/(m_1)+1/(m_1)=1+lambda+mu` none of these

A

`lamda(m_(2)+m_(3))+mu(m_(3)+m_(1))+v(m_(1)+m_(2))=0`

B

`lamda(m_(2)m_(3)-1)+mu(m_(3)m_(1)-1)+v(m_(1)m_(2)-1)=0`

C

Both (a) and (b)

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|21 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise For Session 7|18 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos

Similar Questions

Explore conceptually related problems

Three sided of a triangle have equations L_(1)-=y-m_(i)x=o;i=1,2 and 3. Then L_(1)L_(2)+lambda L_(2)L_(3)+mu L_(3)L_(1)=0 where lambda!=0,mu!=0, is the equation of the circumcircle of the triangle if 1+lambda+mu=m_(1)m_(2)+lambda m_(2)m_(3)+lambda m_(3)m_(1)m_(1)(1+mu)+m_(2)(1+lambda)+m_(3)(mu+lambda)=0(1)/(m_(3))+(1)/(m_(1))+(1)/(m_(1))=1+lambda+mu none of these

Equation of the circumcircle of a triangle formed by the lines L_(1)=0,L_(2)=0andL_(3)=0 can be written as L_(1)L_(2)+lamdaL_(2)L_(3)+muL_(3)L_(1)=0 , where lamdaandmu are such that coefficient of x^(2) =coefficient of y^(2) and coefficient of xy=0. If L_(1)L_(2)+lamdaL_(2)L_(3)+muL_(3)L_(1)=0 is such that mu=0andlamda is non-zero, then it represents

If lambda be the ratio of the roots of the quadratic equation in x,3m^(2)x^(2)+m(m-4)x+2=0 then the least values of m for which lambda+(1)/(lambda)=1 is

Two sides of a triangle are y=m_(1)x and y=m_(2)x and m_(1),m_(2), are the roots of the equation x^(2)+ax-1=0. For all values of a, the orthocentre of the triangle lies at (A)(1,1) (B) (2,2) (C) ((3)/(2),(3)/(2)) (D) (0,0)

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

If y+3=m_1(x+2) and y+3=m_2(x+2) are two tangents to the parabola y_2=8x , then (a)m_1+m_2=0 (b) m_1+m_2=-1 (c)m_1+m_2=1 (d) none of these

If the points A(-1, 3, lambda), B(-2, 0, 1) and C(-4, mu, -3) are collinear, then the values of lambda and mu are

Prove that the three lines from O with direction cosines l_1, m_1, n_1: l_2, m_2, n_2: l_3, m_3, n_3 are coplanar, if l_1(m_2n_3-n_2m_3)+m_1(n_2l_3-l_2n_3)+n_1(l_2m_3-l_3m_2)=0

ARIHANT MATHS-CIRCLE -Exercise (Single Option Correct Type Questions)
  1. The difference between the radii of the largest and smallest circles w...

    Text Solution

    |

  2. The number of rational point(s) [a point (a, b) is called rational, if...

    Text Solution

    |

  3. Three sided of a triangle have equations L1-=y-mi x=o; i=1,2a n d3. Th...

    Text Solution

    |

  4. f(x , y)=x^2+y^2+2a x+2b y+c=0 represents a circle. If f(x ,0)=0 has e...

    Text Solution

    |

  5. If (1+ax)^n = 1 + 8x + 24x^2 + … and a line through (a, n) cuts the ci...

    Text Solution

    |

  6. A region in the x-y plane is bounded by the curve y=sqrt(25-x^2) and t...

    Text Solution

    |

  7. S(x,y)=0 represents a circle. The equation S(x,2)=0 gives two identica...

    Text Solution

    |

  8. Let 0 lt alpha lt (pi)/(2) be a fixed angle . If p=(costheta, sin the...

    Text Solution

    |

  9. Find the number of point (x ,y) having integral coordinates satisfying...

    Text Solution

    |

  10. The point ( [P + 1] , [P] ) (where [.] denotes the greatest integer fu...

    Text Solution

    |

  11. A point Plies inside the circles x^2+y^2-4=0 and x^2+y^2-8x+7=0. The...

    Text Solution

    |

  12. The set of values of 'c' so that the equations y=|x|+c andx^(2)+y^(2)-...

    Text Solution

    |

  13. If a line segement A M=a moves in the plane X O Y remaining parallel t...

    Text Solution

    |

  14. Show that the four points of intersection of the lines : (2x-y + 1) (x...

    Text Solution

    |

  15. Find the number of integral values of lambda for which x^2+y^2+lambdax...

    Text Solution

    |

  16. Let phi(x,y)=0 be the equation of a circle. If phi(0,lamda)=0 has equa...

    Text Solution

    |

  17. Find the locus of the point of intersection of tangents to the circle ...

    Text Solution

    |

  18. One of the diameter of a circle circumscribing the rectangle ABCD is 4...

    Text Solution

    |

  19. A, B C and D are the points of intersection with the coordinate axes o...

    Text Solution

    |

  20. alpha,beta and gamma are parametric angles of three points P, Q and R ...

    Text Solution

    |