The area of the triangle formed by the tangents from (1, 3) to the circle x²+y²-4x+6y+1=0 and its chord of contact is

The condition that the pair of tangents drawn from (g, f) to the circle x²+y²+2gx+2fy+c=0 may be at right angles is

The equation of the circle passing through the points of intersection of the circles x²+y²-8x+10y+2=0, x²+y²-3x+5y-1=0 and touching line 2x+y=3 is

The equation of the circle passing the origin having its centre on the line x+y=4 and cutting the circle x²+y²-4x+2y+4=0  orthogonally is

The limiting points of the coaxal system x²+y²+2λx+4=0 are

The equation of the circle passing  through (2, 1) and touching the coordinate axes is

The length of the tangent from the point (-1, 1) to the circle x²+y²-4x+k=0 is equal to 2 then k=

The equations of the tangents to the circle x²+y²=16 which are inclined at an angle of 60⁰ to the x-axis is

The common chord of x²+y²-4x-4y=0 and x²+y²=16 substends at the origin an angle equal to

The conjugate line of 3x+4y-45=0 with respect to x²+y²-6x-8y+5=0 which is perpendicular to x+y=0 is