The squared length of the intercept made by the line `x=h` on the pair of tangents drawn from the origin to the circle `x^2+y^2+2gx+2fy+c=0` is `(4c h^2)/((g^2-c)^2)(g^2+f^2-c)` `(4c h^2)/((f^2-c)^2)(g^2+f^2-c)` `(4c h^2)/((f^2-f^2)^2)(g^2+f^2-c)` (d) none of these

The condition that the pair of tangents drawn from origin to circle x^(2)+y^(2)+2gx+2fy+c=0 may be at right angles is

If the length of the tangent drawn from (f, g) to the circle x^2+y^2= 6 be twice the length of the tangent drawn from the same point to the circle x^2 + y^2 + 3 (x + y) = 0 then show that g^2 +f^2 + 4g + 4f+ 2 = 0 .

The distance between the chords of contact of tangents to the circle x^2+y^2+2gx +2fy+c=0 from the origin & the point (g,f) is

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

If the length of the tangent from a point (f,g) to the circle x^2+y^2=4 be four times the length of the tangent from it to the circle x^(2)+y^(2)=4x , show that 15f^(2)+15g^(2)-64f+4=0

If the angle between the tangents drawn to x^2+y^2+2gx+2fy+c=0 from (0, 0) is pi/2, then g^2+f^2=3c g^2+f^2=2c g^2+f^2=5c g^2+f^2=4c

Show that the condition that the circle x^2+y^2+2g_1x+2f_1y+c_1=0 bisects the circumference of the circle x^2+y^2+2g_2x+2f_2y+c_2=0 is 2(g_1-g_2)g_2+2(f_1-f_2)f_2=c_1-c_2

The equation of the circumcircle of an equilateral triangle is x^2+y^2+2gx+2fy+c=0 and one vertex of the triangle in (1, 1). The equation of the incircle of the triangle is a. 4(x^2+y^2)=g^2+f^2 b. 4(x^2+y^2)+8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f) c. 4(x^2+y^2)+8gx+8fy=g^2+f^2 d. None of These

The circle x^2+y^2+2gx+2fy+c=0 does not intersect x-axis , if (a) g^2ltc (b) g^2gt c (c) g^2<2c (d) none of these

If two circles x^2+y^2+2gx+2fy=0 and x^2+y^2+2g'x+2f'y=0 touch each other , then ((f')/(f))(g/(g')) =___