If the lines x+2y+k=0, x+y-3=0 are conjugate w.r.t the circle x²+yu²=9 then k=

If the length of the tangent from (2, 3) to circle x²+y²+6x+2ky-6=0 is equal to 7. Then k=

Let A and B be any two points on each of the circles x²+y²-8x-8y+28=0 and x²+y²-2x-3=0 respectively. If d is the distance between A and B then the set of all possible values of d is

The length and the midpoint of the chord 2x+y-5=0 w.r.t the circle x²+y²=9 is

For the circle x²+y²-2x-4y-4=0 the lines 2x+3y-1=0, 2x+y+5=0 are

If a tangent drawn from the point (4, 0) to the circle x²+y²=8 touches it at a point in the first quadrant, then the coordinates of another point B on the circle such that AB=4 are

For the circle x²+y²-6x-6y+5=0 the lines 3x+y-2=0, x+7y-11=0 are

The condition that the circles x²+y²+2ax+c=0, x²+y²+2by+c=0 may touch each other is

If the circles described on the line joining the points (0, 1) and (α, β) as diameter cuts the axis of x in points whose abscissa are the roots of the equation x²-5x+3=0, then (α, β)=

The point of intersection of the tangents to the circle passing through (4, 7), (5, 6). (1, 8) at the points where it is cut by the line 5x+y+17=0 is