The locus of the mid-points of the chords of x^2 + y^2 + 4x - 6y -12 =0 which subtend an angle of pi/3 at its circumference is (1){x-2}^2 + {y+3}^2=6.25 (2){x+2}^2 + {y-3}^2=6.25 (3){x+2}^2 + {y-3}^2=6.25 (4){x+2}^2 + {y+3}^2=6.25{*plese explen*}

Only equal chords subtend equal angles at the centre. Find the distance between centre of circle and the mid point of chord. The locus will be a circle woth same centre and radius equal to the the distance between centre and the mid point.
Also, the angle subtend at the centre is pi/3. So, equilateral triangle is formed among the 2 radii arms and the chord. Use this information to find the length of perpendicular (length of altitude in an equilateral triangle.)
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