The line `x+2y+3=0` cuts the circle `x^2+y^2+4x+4y=1` at P and Q, and the line `2x+3y+lambda=0` cuts the circle `x^2+y^2+6x+2y=7` at R and S. If P, Q, R and S are concyclic then `lambda` is equal to

The line Ax+By+=0 cuts the circle by x^2+y^2+Ax+By+C=0at P and Q. The line A'x +B'x+C'=0 cuts the circle x^2+y^2+a'x+b'y+c'=0 at R and S.If P,Q, R and S are concyclic then show that det (( a-a", b-b',c-c'),(A,B,C),(A',B',C'))=0

The line x+3y=0 is a diameter of the circle x^(2)+y^(2)+6x+2y=0

The line x+3y=0 is a diameter of the circle x^(2)+y^(2)-6x+2y=0

The line 4y-3x+lambda=0 touches the circle x^(2)+y^(2)-4x-8y-5=0 then lambda=

A circle touching the line x +y - 2 = 0 at (1,1) and cuts the circle x^(2) +y^(2) +4x +5y - 6 = 0 at P and Q. Then

Find the image of the circle x^(2)+y^(2)-2x+4y-4=0 in the line 2x-3y+5=0

A tangent to the circle x^(2)+y^(2)=1 through the point (0, 5) cuts the circle x^(2)+y^(2)=4 at P and Q. If the tangents to the circle x^(2)+y^(2)=4 at P and Q meet at R, then the coordinates of R are

If the line y-sqrt(3)x+3=0 cuts the parabola y^(2)=x+2 at P and Q then AP.AQ is equal to