The  length of the latus rectum of the parabola 289(x−3)2+(y−1)2=(15x−8y+13)2  is equal to

We can write the given equation  as(x−3)2+(y−1)2=|15x−8y+13|17This represents a parabola with focus at (3, 1) and directrix as 15x-8y+ 13 =0.L= length of latus rectum=2[distance of focus from the directrix]=2|15(3)−8(1)+13|17=10017≃5.88