Find the equation to the locus of mid-points of chords drawn through the point (a, 0) on the circle `x^(2) + y^(2) = a^(2)`.

Find the equation to the locus of mid-points of chords drawn through the point (0, 4) on the circle x^(2) + y^(2) = 16 .

Find the equation to the chord of contact of the tangents drawn from an external point (-3, 2) to the circle x^2 + y^2 + 2x-3=0 .

Find the equation to the chord of contact of the tangents drawn from an external point (-3, 2) to the circle x^2 + y^2 + 2x-3=0 .

Find the equation to the chord of contact of the tangents drawn from an external point (-3, 2) to the circle x^2 + y^2 + 2x-3=0 .

Find the length and mid-point of the chord 2x+ y-5 with respect to the circle x^(2) +y^(2) =9,

Find the locus of mid-point of chords to the circle (x−3)^2+(y−2)^2=1 which pass through (3,7)

The locus of the mid points of the chords passing through a fixed point (alpha, beta) of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 is

(i) Find the equation of that chord of the circle x^(2) + y^(2) = 15 , which is bisected at the point (3,2). (ii) Find the locus of mid-points of all chords of the circle x^(2) + y^(2) = 15 that pass through the point (3,4),