Tangents are drawn to the circles `x^(2)+y^(2)+4x+6y-19=0,x^(2)+y^(2)=9` from any point on the 2x+3y=5. Prove that their lengths are equal.

Find the radius of the circle x^(2)+y^(2)-4x-6y+12=0

Prove that the circles x^(2) +y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(2) - 10x - 6y + 14 = 0 touch at the point (3,-1)

The common tangents to the circles x^2 + y^2 + 2x =0 and x^2 + y^2-6x=0 form a triangle which is

Find the parametric equation of the circles : 3x^2 + 3y^2+4x-6y-4=0 .

The number of common tangents to the circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+6x+18y+26=0 , is

Find the angle between the circles S:x^(2)+y^(2)-4x+6y+11=0andS':x^(2)+y^(2)-2x+8y+13=0

The line 3x -4y = k will cut the circle x^(2) + y^(2) -4x -8y -5 = 0 at distinct points if

If the pair of tangents are drawn from the point (4,5) to the circle x^(2)+y^(2)-4x-2y-11=0 , then (i) Find the length of chord of contact. (ii) Find the area of the triangle fromed by a pair of tangents and their chord of contact. (iii) Find the angle between the pair of tangents.

The point of tangency of the circles x^2+ y^2 - 2x-4y = 0 and x^2 + y^2-8y -4 = 0 , is

The equation of tangent drawn to the curve y^(2)-2x^(3)-4y+8=0 from the point (1, 2) is given by