Find the condition that the circle `(x-3)^2+(y-4)^2=r^2` lies entirely within the circle `x^2+y^2=R^2` .

Find the center of circle (x+2)^2+(y+4)^2=16

The length of the tangent from any point on the circle (x-3)^2 + (y + 2)^2 =5r^2 to the circle (x-3)^2 + (y + 2)^2 = r^2 is 4 units. Then the area between the circles is

If the circle x^2+y^2+2a_1x+c=0 lies completely inside the circle x^2+y^2+2a_2x+c=0 then

If the pole of the line with respect to the circle x^(2)+y^(2)=c^(2) lies on the circle x^(2)+y^(2)=9c^(2) then the line is a tangent to the circle with centre origin is

Show that the circle x^2+y^2+4x+4y-1=0 bisects the circumference of the circle x^2+y^2+2x-3=0 .

Find the condition, that the line lx + my + n = 0 may be a tangent to the circle (x - h)^(2) + (y - k)^(2) = r^(2) .

There are two perpendicular lines, one touches to the circle x^(2) + y^(2) = r_(1)^(2) and other touches to the circle x^(2) + y^(2) = r_(2)^(2) if the locus of the point of intersection of these tangents is x^(2) + y^(2) = 9 , then the value of r_(1)^(2) + r_(2)^(2) is.

If the pole of a straight line with respect to the circle x^(2)+y^(2)=a^(2) lies on the circle x^(2)+y^(2)=9a^(2) , then the straight line touches the circle

If the pole of a line w.r.t to the circle x^(2)+y^(2)=a^(2) lies on the circle x^(2)+y^(2)=a^(4) then find the equation of the circle touched by the line.

The locus of poles of tangents to the circle (x-p)^(2)+y^(2)=b^(2) w.r.t. the circle x^(2)+y^(2)=a^(2) is