The chords through (2,1) to the circle `x^2-2x+y^2-2y+1=0` are bisected at the point `(alpha,1/2)` then value of `(2alpha)/3` is ___

Chord of the circle x ^(2) +y ^(2) = 81 bisected at the point (-2,3) meets the diameter x + 5y =0 at a point

If x/alpha+y/beta=1 touches the circle x^2 +y^2=a^2 , then point (1/alpha,1/beta) lies on a/an

The midpoint of the chord y=x-1 of the circle x^(2)+y^(2)-2x+2y-2=0 is

The chord of the circle x^(2)+y^(2)-y^(2)-4x=0 which is bisected at (1,0) is perpendicular to the line

If circle x^(2)+y^(2)-x+3y+m=0 bisect the circumference of circle x^(2)+y^(2)-2x+2y+1=0 then value of m is

If the chord of contact of tangents from a point (x_1,y_1) to the circle x^2+y^2=a^2 touches the circle (x-a)^2+y^2=a^2 , then the locus of (x_1,y_1) is :

If the chord of contact of tangents from a point (x_1, y_1) to the circle x^2 + y^2 = a^2 touches the circle (x-a)^2 + y^2 = a^2 , then the locus of (x_1, y_1) is

The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing through the origin and touching the line y=x always passes through the point. (a) (-1/2,1/2) (b) (1, 1) (c) (1/2,1/2) (d) none of these

The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing through the origin and touching the line y=x always passes through the point. (a) (-1/2,1/2) (b) (1, 1) (c) (1/2,1/2) (d) none of these