Show that the circle `S-= x^(2) + y^(2) + 2gx +`
` 2fy + c = 0` touches the
(i) X- axis if `g^(2) = c`

If the circle x^(2) + y^(2) + 2g x + 8y + 16 = 0 touches the x axis, then the values of g are

The circle x^(2) + y^(2) + 2g x + 2fy + c = 0 does not intersect the y-axis if

Prove that the circle x^(2) +y^(2) - 6 x -2 y + 9 = 0 (i) touches the x-axis, (ii) lies entirely inside the circle x^(2) + y^(2) = 18 .

Show that the circle x^(2)+y^(2)-2ax-2ay+a^(2)=0 touches both the coordinate axes.

Find the conditions that the line (i) y = mx + c may touch the circle x^(2) +y^(2) = a^(2) , (ii) y = mx + c may touch the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 .

Find the centre and radius of the circle ax^(2) + ay^(2) + 2gx + 2fy + c = 0 where a ne 0 .

If the point (2,-3) lies on the circle x^(2) + y^(2) + 2 g x + 2fy + c = 0 which is concentric with the circle x^(2) + y^(2) + 6x + 8y - 25 = 0 , then the value of c is

If the circle x^(2) +y^(2) + 2gx + 2fy + c = 0 bisects the circumference of the circle x^(2) +y^(2) + 2g'x + 2f'y + c' = 0 , them the length of the common chord of these two circles is

The polar of p with respect to a circle s=x^(2)+y^(2)+2gx+2fy+c=0 with centre C is

Find the pair of tangents from the origin to the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 and hence deduce a condition for these tangents to be perpendicular.