Show that the equation of the circle which touches the coordinates axes whose centre lies on the line `l x+m y+n=0\ i s\ (l+m)^2 (x^2 + y^2 )+2n(x+y)(l+m)+n^2=0.`

Find the equation of the circle which touches the coordinate axes and whose centre lies on the line x-2y=3.

Find the equation of the circle which touches the coordinate axes and whose centre lies on the line x-2y = 3 .

Find the equation of the circle which touches the lines 4x-3y+10=0a n d4x-3y-30=0 and whose centre lies on the line 2x+y=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 straight line through the point (alpha,beta) and perpendiculasr to the line l x+m y+n=0.

(i) Find the equation of a circle which touches both the axes and whose centre is (2,2). (ii) Find the equation of a circle, touching the lines x=0, y=0 and x=6.

Find the locus of the centre of the circle touching the line x+2y=0a n d x=2y

The equation of the circle of radius 2sqrt(2) whose centre lies on the line x-y=0 and which touches the line x+y=4 , and whose centre is coordinate satisfy x+ygt4 , is

The equation of the plane through the intersection of the plane a x+b y+c z+d=0\ a n d\ l x+m y+n+p=0 and parallel to the line y=0,\ z=0. (A) (b l-a m)y+(c l-a n)z+d l-a p=0 (B) (a m-b l)x+(m c-b n)z+m d-b p=0 (c) (n a-c l)d+(b n-c m)y+n d-c p=0 (D) None of these

Find the direction cosines of the lines, connected by the relations: l+m+n=0 and 2l m+2ln-m n=0.