The lilne `y=mx+x` and the circle `x^(2)+y^(2)=a^(2)` intersect at A and B. If `AB=2lambda`, then show that : `c^(2)=(1+m^(2))(a^(2)-lambda^(2))`.

If y = mx + c and x^(2) + y^(2) = a^(2) intersect at A and B and if AB = 2lambda , then show that c^(2) =( 1+ m^(2)) (a^(2) - lambda ^(2))

The line y=mx+c intersects the circle x^(2)+y^(2)=r^(2) in two distinct points if

If the line y=mx+asqrt(1+m^2) touches the circle x^2+y^2=a^2 , then the point of contact is

If the straight line y=mx is outside the circle x^(2)+y^(2)-20y+90=0 , then show that |m|lt3 .

If the circles x^2+y^2+2x+2ky+6=0 and x^2+y^2+2ky+k=0 intersect orthogonally, show that k=2 or -3/2

If the circles (x-1)^(2)+(y-3)^(2)=4r^(2) and x^(2)+y^(2)-8x+2y+8=0 intersect in two distinct points, then show that 1ltrlt 4 .

If the straight line represented by x cos alpha + y sin alpha = p intersect the circle x^2+y^2=a^2 at the points A and B , then show that the equation of the circle with AB as diameter is (x^2+y^2-a^2)-2p(xcos alpha+y sin alpha-p)=0

If two circles x^(2)+y^(2)+2a_(1)x+2b_(1)y=0 and x^(2)+y^(2)+2a_(2)x+2b_(2)y=0 touches then show that a_(1)b_(2)=a_(2)b_(1)

The length of the common chord of the circles (x - a)^(2) + (y - b)^(2) =c^2" and " (x -b)^(2) + (y -a)^(2) = c^(2) = c^(2) is