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))`.

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

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 y -axis then the condition is

Locus of the middle point of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 Which passes through a fixed point (alpha,beta) is hyperbola whose centre is (A) (alpha,beta) (B) (2 alpha,2 beta) (C) ((alpha)/(2),(beta)/(2)) (D) none

Prove that the locus of the middle-points of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which pass through a fixed point (alpha, beta) is a hyperbola whose centre is ((alpha)/(2), (beta)/(2)) .

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.

Show that the length of the tangent from anypoint on the circle : x^2 + y^2 + 2gx+2fy+c=0 to the circle x^2+y^2+2gx+2fy+c_1 = 0 is sqrt(c_1 -c) .

I If a point (alpha,beta) lies on the circle x^(2)+y^(2)=1 then the locus of the point (3 alpha.+2,beta), is