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 _________.

Answer

7

Explanation

(7) Here, `(x-1)^(2)+(y-3)^(2)={(5x-12+17)/(sqrt(5^(2))+(-12)^(2))}^(2)`
Therefore, the is (1,3) and directrix is 5x-12y+17=0.
The distance of the focus from the directrix is
`|(5xx1-12xx3+17)/(sqrt(5^(2)+(-12)^(2)))|=(14)/(13)`
`:." Length of latus rectum"=2xx(14)/(13)=(28)/(13)`