An equation of the chord of the circle x2+y2=a2  passing through the point (2, 3)  farthest from the centre is

Let P(2, 3)  be the given point, M be the middle point of a chord of the circle x2+y2=a2 through P.Then the distance of the centre O of the circle from the chord is OM.and (OM)2=(OP)2−(PM)2Which is maximum when PM is minimum i.e, M coincides with p i.e. P is the middle point of the chord.Hence the equation of the chord is 2.x+3.y−a2=(2)2+(3)2−a2 ⇒2x+3y=13