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` .

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

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

Find the condition for the line lx + my + n =0 is a tangent to the circle x^(2) + y^(2) = a^(2)

Find the equation of the circles whose radius is 4 and whish is concentric with the circle x^(2)+y^(2)+2x-6y=0

Find the middle point of the chord of the circle x^2+y^2=25 intercepted on the line x-2y=2

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

If the tangents are drawn to the circle x^2+y^2=12 at the point where it meets the circle x^2+y^2-5x+3y-2=0, then find the point of intersection of these tangents.

Find the equation of the normal to the circle x^2+y^2-2x=0 parallel to the line x+2y=3.

Tangents are drawn to the circle x^2+y^2=9 at the points where it is met by the circle x^2+y^2+3x+4y+2=0 . Fin the point of intersection of these tangents.

Find the equation of a circle with center (4, 3) touching the circle x^2+y^2=1