Find the equation of a circle circumscribing the triangle whose sides are `x=0, y=0 and lx + my = 1`. If `l, m` can vary so that `l^2 + m^2 = 4l^2 m^2`, find the locus of the centre of the circle.

Find the equation of a circle circumscribing the triangle whose sides are 2x+y-3=0, 3x-y-7=0 and x-2y+1=0.

Find the equation of the circle which circumscribes the triangle formed by the lines x=0,\ y=0\ a n d\ l x+m y=1.

Find the equation of the circle circumscribing the triangle formed by the lines x + y + 1 = 0, 3 x + y - 5 = 0, and 2 x + y - 4 = 0.

Find the equation of the circle which circumscribes the triangle formed by the line: 2x+y-3=0,\ x+y-1=0\ a n d\ 3x+2y-5=0\

Find the equation of circle whose centre is the point (1,- 3) and touches the line 2x-y-4=0

Prove that the locus of the circumcentre of the variable triangle having sides y-axis, y = 2 and lx + my = 1 where (l, m) lies on the parabola y^(2)=4ax , is also a parabola

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

Consider the following lines : L_(1) : x-y-1=0 L_(2):x+y-5=0 L_(3):y-4=0 Let L_(1) is axis to a parabola, L_(2) is tangent at the vertex to this parabola and L_(3) is another tangent to this parabola at some point P. Let 'C' be the circle circumscribing the triangle formed by tangent and normal at point P and axis of parabola. The tangent and normals at normals at the extremities of latus rectum of this parabola forms a quadrilateral ABCD. Q. The equation of the circle 'C' is :

Find the equation of the largest circle with centre (1, 0) that can be inscribed in the ellipse x^2 + 4y^2 = 16

Find the angle between the line whose direction cosines are given by l+m+n=0a n dl^2+m^2-n^2-0.