Parabola

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The length of the latus rectum of the parabola $289 \{(x - 3)^{2} + (y - 1)^{2}\} = (15 x - 8 y + 13)^{2}$ is equal to

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Solution

We can write the given equation as
$\sqrt{(x - 3)^{2} + (y - 1)^{2}} = \frac{| 15 x - 8 y + 13 |}{17}$
This 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]
$= 2 \frac{| 15 (3) - 8 (1) + 13 |}{17} = \frac{100}{17} ≃ 5 .88$

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Parabola

Remember concepts with our Masterclasses.

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

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The length of the latus rectum of the parabola $289 \{(x - 3)^{2} + (y - 1)^{2}\} = (15 x - 8 y + 13)^{2}$ is equal to