The straight line x-2y+1=0intersects the line circle x²+y²=25 in points P and Q, the coordinates of the point of intersection of tangents drawn at P and Q to the circle is

If the tangents at (3, -4) to the circle x²+y²-4x+2y-5=0 w.r.t the circle x²+y²+16x+2y+10=0 in A and B, then the midpoint of AB is

The polar of (x₁, y₁) w.r.t the circle x²+y²=a² meets the coordinate axes in A and B. The area of ΔOAB is

The equations of the tangents drawn from the origin x²+y²+2gx+2fy+f²=0 is

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