From any point on the circle x²+y²+2gx+2fy+c=0 tangents are drawn to the circle x²+y²+2gx+2fy+c sin²α+(g²+f²) 13cos² α =0

The area of the triangle formed by the positive x-axis and the tangent and the normal at (1, √3) to the circle x²+y²=4 is

The locus of the points from which the lengths of the tangents to the two circles x² + y² + 4x + 3 = 0, x² + y²-6x +5 = 0 are in the ratio 2 : 3 is a circle with centre

The equation to the line joining the centers of the circles belonging to the coaxial system of Circles 4x²-4y²-12x+ 6y-3+λ(x+2y-6)=0 is

x²+y²-4x-6y+9=0 and (x+3)²+(y+2)²=25 are two circles. The line x=2 is a

The equation of the circle passing through the point (1, -2) and having its centre on the line 2x-y-14=0 and touching the line4x+3y-23=0 is

The equation to the pair of tangents drawn from (3, 2) to the circle x²+y²-6x+4y-2=0 is

The equation of one tangent to the circle with Centre(2,-1) from the origin is 3x + y = 0, then the equation of the other tangent through the origin is

The equation to the circle which is such that the lengths of the tangents to it from the points (1,0), (2,0) and (3,2)are 1,√7, √2, respectively is

The locus of the centre of the circles which touché both the circles x²+y²=a² and x²+y²=4ax externally has the equation