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If the length of the latus rectum rectum...

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 _________.

Text Solution

Verified by Experts

The correct Answer is:
7
(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)`
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Knowledge Check

  • The length of the latusrectum of the parabola 169{(x - 1)^(2) + (y - 3)^(2)} = (5x - 12y + 17)^(2) is

    A
    `14/13`
    B
    `12/13`
    C
    `28/13`
    D
    none

  • The length of the latus rectum of the parabola 169{(x-1)^2+(y-3)^2}=(5x-12y+17)^2 is

    A
    `(12)/(13)`
    B
    `(14)/(13)`
    C
    `(28)/(13)`
    D
    none

  • The length of the latusretum of the parabola 169|(x-1)^(2)+(y-3)^(2)|=(5x-12y+7)^(2) , is

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

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