The length of the shortest chord of the circles `x^2 +y^2+2gx + 2fy+c=0 ` which passes through the point (a, b) inside the circle is

Show that the length of the least chord of the circle x^2+y^2+2gx+2fy+c=0 which passes through an internal point (alpha, beta) is equal to 2sqrt(-(alpha^2+beta^2+2galpha+2fbeta+c)) .

Show that the length of the least chord of the circle x^2+y^2+2gx+2fy+c=0 which passes through an internal point (alpha, beta) is equal to 2sqrt(-(alpha^2+beta^2+2galpha+2fbeta+c)) .

locus of the middle point of the chords of the circle x^(2)+y^(2)+2gx+2fy+c=0 which passed through a fixed point (a,b)

If the circle x ^(2) + y^(2) + 2gx + 2fy+ c=0 touches X-axis, then

If the circle x ^(2) + y^(2) + 2gx + 2fy+ c=0 touches X-axis, then

If the origin lies inside the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 , then

Find the locus of the mid-point of the chords of the circle x^2 + y^2 + 2gx+2fy+c=0 which subtend an angle of 120^0 at the centre of the circle.

Find the locus of the mid-point of the chords of the circle x^2 + y^2 + 2gx+2fy+c=0 which subtend an angle of 120^0 at the centre of the circle.

Find the equation of chord of the circle x^(2)+y^(2)-2x-4y-4=0 passing through the point (2,3) which has shortest length.

Find the equation of chord of the circle x^(2)+y^(2)-2x-4y-4=0 passing through the point (2,3) which has shortest length.