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

The incentre of an equilateral triangle is ( 1, 1) and the equation of the one side is 3x + 4y + 3 = 0 . Then the equation of the circumcircle of the triangle is

The incentre of an equilateral triangle is (1,1) and the equation of one side is 3x + 4y + 3 = 0 . Then the equation of the circumcircle of the triangle is _

If the locus of the circumcentre of variable triangle having sides x = 0 , y = 2 and lx + my = 1 where (l , m) lies on the Parabola y^(2) = 4 ax is a curve 'C' then Coorrdinates of the vertex of this curve 'C' is _

What is shape of the orbital with (i) n = 2 and l = 0 , (ii) n = 2 and l = 1?

Let L_1-=ax+by+aroot(3)(b)=0 and L_2-=bx+ay+aroot(3)(a)=0 be two straight lines. The equations of the bisectors of the angle formed by the lines whose equations are lambda_1L_1-lambda_2L_2=0 and lambda_1L_1+lambda_2L_2=0 and lambda_1 and lambda_2 being non zero real numbers, are given by

The equations of bisectors of two lines L_1 & L_2 are 2x-16y-5=0 and 64x+ 8y+35=0 . lf the line L_1 passes through (-11, 4) , the equation of acute angle bisector of L_1 & L_2 is:

theta_1 and theta_2 are the inclination of lines L_1 and L_2 with the x-axis. If L_1 and L_2 pass through P(x_1,y_1) , then the equation of one of the angle bisector of these lines is

The locus of the circumcenter of a variable triangle having sides the y-axis, y=2, and lx+my=1, where (l,m) lies on the parabola y^(2)=4x , is a curve C. The coordinates of the vertex of this curve C is

Consider the line L 1 : x 1 y 2 z 1 312 +++ ==, L2 : x2y2z3 123

Consider the line L 1 : x 1 y 2 z 1 312 +++ ==, L2 : x2y2z3 123