From the point A(0,3) on the circle x²+4x+(y-3)²=0, a chord, AB is drawn and extended to a point P, such that AP = 2AB. The locus of P is

If α,β,γ are the roots of x³-x²+33x+5=0 and A=s₁,B=s₂,C=s₃ then the descending order of A,B,C is

If the circles x²+y²+2x-2y+4=0 cuts the circle x²+y²+4x-2fy+2=0 orthogonally, then f=

If the circles x²+y²-4x+6y+8=0, x²+y²-10x-6y+14=0 touch each other , then the point of contact is

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