If the chord `x + 2y - 2 = 0` of the curve `6x² + y^2 - 8x + 2y = 0` subtends angle `pi/k` radians at the point `(1, 1)` then the value of `k` is

If the chord y=m x+1 of the circles x^2+y^2=1 subtends an angle of 45^0 at the major segment of the circle, then the value of m is

The locus of the mid points of the chords of the circle x^2+y^2+4x-6y-12=0 which subtends of angle of pi/3 radians at its centre is

The chord along the line y-x=3 of the circle x^2 + y^2 = k^2 , subtends an angle of 30^0 in the major segment of the circle cut off by the chord. Find k .

The chord along the line y-x=3 of the circle x^2 + y^2 = k^2 , subtends an angle of 30^0 in the major segment of the circle cut off by the chord. Find k .

If the curves x^2-6x+y^2+8=0 and x^2-8y+y^2+16 -k =0 , (k gt 0) touch each other at a point , then the largest value of k is ________.

If the curves x^2-6x+y^2+8=0 and x^2-8y+y^2+16 -k =0 , (k gt 0) touch each other at a point , then the largest value of k is ________.

The equation of the locus of the mid-points of chords of the circle 4x^2 + 4y^2-12x + 4y +1= 0 that subtends an angle of (2pi)/3 at its centre is x^2 + y^2-kx + y +31/16=0 then k is

The equation of the locus of the mid-points of chords of the circle 4x^2 + 4y^2-12x + 4y +1= 0 that subtends an angle of at its centre is (2pi)/3 at its centre is x^2 + y^2-kx + y +31/16=0 then k is

The equation of the locus of the mid-points of chords of the circle 4x^2 + 4y^2-12x + 4y +1= 0 that subtends an angle of (2pi)/3 at its centre is x^2 + y^2-kx + y +31/16=0 then k is