The equation of chord with mid-point `P(x_(1),y_(1))` to the circle `S=0` is

STATEMENT-1 : The equation of chord of circle x^(2) + y^(2) - 6x + 10y - 9 = 0 , which is be bisected at (-2, 4) must be x + y = 2. and STATEMENT-2 : The equation of chord with mid-point (x_(1), y_(1)) to the circle x^(2) + y^(2) = r^(2) is xx_(1) + yy_(1) = x_(1)^(2) + y^(2) .

The equation of tangent at P(x_(1),y_(1)) to the circle S=0 is given by

The length of the chord of contact of the point P(x_(1),y_(1)) w.r.t.the circle S=0 with radius r is

The equation of pair of tangents drawn from an external point P(x_(1),y_(1)) to circle S=0 is

The equation of the chord of the circle S=0 whose midpoint is (x_(1),y_(1)) is

The equation of the locus of the mid-points of chords of the circle 4x^(2) + 4y^(2) -12x + 4y + 1 = 0 that substend an angle (2pi)/(3) at its centre, is

Area of triangle formed by two tangents from (x_(1),y_(1)) to the circle S=0 and chord of contact of (x_(1),y_(1)) is,(r is radius of circle)

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

From the origin,chords are drawn to the circle (x-1)^(2)+y^(2)=1. The equation of the locus of the mid-points of these chords is circle with radius