If the length of the latus rectum rectum of the parabola `169{(x-1)^(2)+(y-3)^(2)}=(5x-12y+17)^(2)` is L then the value of 13L/4 is _________.

Options

A. `14/13`
B. `28/13`
C. `12/13`
D. `48/13`

Answer

D

Explanation

The equation of the parabola is `sqrt((x-1)^(2)+(y-3)^(2))=|(5x-12y+7)/(sqrt(5^(2)+(-12)^(2)))|`
Clearly, its focus is (1, 3) and the equation of the directrix is 5x-12y=0.
`:." Length of the latusrectum " = 2 xx" Length of the perpendicualr from the focus (1, 3) on the directrix"`
`rArr" Length of the latusrectum = 2"|(5xx1-12xx3+7)/(sqrt(5^(2)+(-12)^(2)))|=48/13`