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

Three sided of a triangle have equations L_1-=y-m_i x=o; i=1,2 and 3. 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 (a) 1+lambda+mu=m_1m_2+lambdam_2m_3+lambdam_3m_1 (b) m_1(1+mu)+m_2(1+lambda)+m_3(mu+lambda)=0 (c) 1/(m_3)+1/(m_1)+1/(m_1)=1+lambda+mu (d)none of these

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

Three sides of a triangle have the equation L_i = y - m_i x = 0 , I = 1, 2, 3. Then L_1L_2 + lambdaL_2L_3 +_ muL_3L_1 = 0 (where lambda ne 0, mu ne 0 ). Is the equation of the circumcircle of the triangle if

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

The line l_1 x+ m_1 y+n=0 and l_2 x + m_2 y+n=0 will cut the coordinate axes at concyclic points if (A) l_1 m_1 = l_2 m_2 (B) l_1 m_2 = l_2 m_1 (C) l_1 l_2 = m_1 m_2 (D) l_1 l_2 m_1 m_2 = n^2

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

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

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