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

The Cartesian equation of the plane vecr=(1+lambda-mu)hati+(2-lambda)hatj+(3-2lambda+2mu)hatk is

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

A B C is a triangle where A=(2,3,5)B=(-1,2,2)a n dC(lambda,5mu) , if the median through A is equally inclined to the axes then: lambda=mu=5 (b) lambda=5,mu=7 lambda=6,mu=9 (d) lambda=0,mu=0

Let L_(1) -= ax+by+a root3 (b) = 0 and L_(2) -= bx - ay + b root3 (a) = 0 be two straight lines . The equations of the bisectors of the angle formed by the foci whose equations are lambda_(1)L_(1)-lambda_(2)L_(2)=0 and lambda _(1) l_(1) + lambda_(2) = 0 , lambda_(1) and lambda_(2) being non - zero real numbers ,are given by

Transition between three energy energy levels in a particular atom give rise to three Spectral line of wevelength , in increasing magnitudes. lambda_(1), lambda_(2) and lambda_(3) . Which one of the following equations correctly ralates lambda_(1), lambda_(2) and lambda_(3) ? lambda_(1)=lambda_(2)-lambda_(3) lambda_(1)=lambda_(3)-lambda_(2) (1)/(lambda_(1))=(1)/(lambda_(2))+(1)/(lambda_(3)) (1)/(lambda_(2))=(1)/(lambda_(3))+(1)/(lambda_(1))

A line of slope lambda(0 < lambda < 1) touches the parabola y+3x^2=0 at Pdot If S is the focus and M is the foot of the perpendicular of directrix from P , then tan/_M P S equals (a) 2lambda (b) (2lambda)/(-1+lambda^2) (c) (1-lambda^2)/(1+lambda^2) (d) none of these

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

A line of slope lambda(0 lt lambda lt 1) touches the parabola y+3x^2=0 at P . If S is the focus and M is the foot of the perpendicular of directrix from P , then tan/_M P S equals (A) 2lambda (B) (2lambda)/(-1+lambda^2) (C) (1-lambda^2)/(1+lambda^2) (D) 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. L_(1)L_(2)^(2)+lamdaL_(2)L_(3)^(2)+muL_(1)^(2)=0 represents

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