If `C_1,C_2,a n dC_3` belong to a family of circles through the points `(x_1,y_1)a n d(x_2, y_2)` prove that the ratio of the length of the tangents from any point on `C_1` to the circles `C_2a n dC_3` is constant.

Find the lengths of the tangents drawn from the point. (-1,1) to the circle x^(2)+y^(2)-2x+4y+1=0

Find the lengths of the tangents drawn from the point. (x_(1),y_(1)) to the circle x^(2)+y^(2)+2x=0

The equation to the chord joining two points (x_1,y_1)a n d(x_2,y_2) on the rectangular hyperbola x y=c^2 is:

Find the length of the tangent drawn from any point on the circle x^2+y^2+2gx+2fy+c_1=0 to the circle x^2+y^2+2gx+2fy+c_2=0

Transverse common tangents are drawn from O to the two circles C_1,C_2 with 4, 2 respectively. Then the ratio of the areas of triangles formed by the tangents drawn from O to the circles C_1 and C_2 and chord of contacts of O w.r.t the circles C_1 and C_2 respectively is

if the distances from the origin to the centre of three circles x^2+y^2+2lambda_ix-c^2=0(i=1,2,3) are in G.P. ,then the lengths of the tangents drawn to them from any point on the circle x^2+y^2=c^2 are in

Tangent is drawn at any point (x_1, y_1) other than the vertex on the parabola y^2=4a x . If tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass through a fixed point (x_2,y_2), then

Two circles C_1a n dC_2 both pass through the points A(1,2)a n dE(2,1) and touch the line 4x-2y=9 at B and D , respectively. The possible coordinates of a point C , such that the quadrilateral A B C D is a parallelogram, are (a ,b)dot Then the value of |a b| is_________

C_1 and C_2 are circle of unit radius with centers at (0, 0) and (1, 0), respectively, C_3 is a circle of unit radius. It passes through the centers of the circles C_1a n dC_2 and has its center above the x-axis. Find the equation of the common tangent to C_1a n dC_3 which does not pass through C_2dot

The length of the tangent of the circle x^2+y^2-2x-y -7 = 0 from the point (-1,-3) is