The equation of the line(s) parallel to `x-2y=1` which touch(es) the circle `x^2+y^2-4x-2y-15=0` is (are) (a)`x-2y+2=0` (b) `x-2y-10=0` (c)`x-2y-5=0` (d) 3`x-y-10=0`

The line 4y - 3x + lambda =0 touches the circle x^2 + y^2 - 4x - 8y - 5 = 0 then lambda=

The equation of the line that touches the curves y=x|x| and x^2+(y-2)^2=4 , where x!=0, is:

Suppose a x+b y+c=0 , where a ,ba n dc are in A P be normal to a family of circles. The equation of the circle of the family intersecting the circle x^2+y^2-4x-4y-1=0 orthogonally is (a) x^2+y^2-2x+4y-3=0 (b) x^2+y^2-2x+4y+3=0 (c) x^2+y^2+2x+4y+3=0 (d) x^2+y^2+2x-4y+3=0

Show that the line 5x + 12y - 4 = 0 touches the circle x^(2)+ y^(2) -6x + 4y + 12 = 0

The line x+3y=0 is a diameter of the circle x^2+y^2-6x+2y=0

The equation of the circle which cuts orthogonally the three circles x^2+y^2+4x+2y+1=0, 2x^2+2y^2+8x+6y-3=0, x^2+y^2+6x-2y-3=0 is

Find the equation of the circle which cuts the circles x^2+y^2+4x+2y+1=0, 2(x^2+y^2)+8x+6y-3=0 and x^2+y^2+6x-2y-3=0 orthogonally.

Find the equation of the tangent to the circle x^2+y^2-2x-2y-23=0 and parallel to 2x+y+3=0.

The equation of a circle of radius 1 touching the circles x^2+y^2-2|x|=0 is (a) x^2+y^2+2sqrt(2)x+1=0 (b) x^2+y^2-2sqrt(3)y+2=0 (c) x^2+y^2+2sqrt(3)y+2=0 (d) x^2+y^2-2sqrt(2)+1=0

Find the image of the circle x^2+y^2-2x+4y-4=0 in the line 2x-3y+5=0