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

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

If the points (0,1,-2),(3,lambda,-1) and (mu,-3,4) are collinear,then the value of lambda and mu are given by