The equation of the diameter of the circle x2+y2+2x−4y−11=0 which bisects the chords intercepted on the line 2x−y+3=0 is
We know that the diameter will be perpendicular to the chord because it bisects the chord. Hence the equation of diameter x+2y+k=0 .............(i)
But (i) also passes through the centre of circle (-1,2). Therefore, −1+4+k=0⇒k+−3.
Hence the required equation is x+2y−3=0