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` .

If the circle (x-2) ^(2) + (y -3) ^(2)=a ^(2) lies entirely in the circle x ^(2) + y ^(2) =b ^(2), then

Show that the circle x^(2)+y^(2)-2y-15=0 lies completely within the circle x^(2)+y^(2)-x-30=0

Find the area enclosed by the circle x^(2)+y^(2)=r^(2)

The length of the tangent from any point on the circle to 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

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

The circle (x-r) ^(2) + (y-r) ^(2) =r ^(2) touches

The length of the tangent from any point on the circle to 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

Find the equation of the circle passing through the centre of the circle x^2 +y^2 -4x-6y=8 and being concentric with the circle x^2 +y^2 - 2x-8y=5 .

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 . If the straight line touches the circle x^2+y^2=r^2 , then :