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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 latus rectum of the parabola (y-1)^(2) =- 6( x+2) is_

    A
    2 units
    B
    3 units
    C
    5 units
    D
    6 units

  • The length of latus rectum of the parabola 3x^(2) =- 8y is _

    A
    `(4)/(3)` unit
    B
    `(8)/(3)` unit
    C
    `(2)/(3)` unit
    D
    4 unit

  • The length of latus rectum of the hyperabola 9y^(2) - 4x^(2) = 36 is -

    A
    8 unit
    B
    9 unit
    C
    10 unit
    D
    12 unit

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