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`

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

The centre of the smallest circle touching the circles x^2+ y^2-2y -3=0 and x^2 +y^ 2-8x -18y +93= 0 is:

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

Find the equation of the tangent to the curve y= sqrt(3x-2) which is parallel to the line 4x-2y+5=0.

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=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

The equation of the line that touches the curves y=x|x| and x^2+(y^2-2)^2=4 , where x!=0, is y=4sqrt(5)x+20 (b) y=4sqrt(3)x-12 y=0 (d) y=-4sqrt(5)x-20

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