Parabola

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Question

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

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Solution

$Here, (x - 1)^{2} + (y - 3)^{2} = {\{\frac{5 x - 12 y + 17}{\sqrt{5^{2} + (- 12)^{2}}}\}}^{2}$
$∴ the focus = (1, 3) and the directrix is 5 x - 12 y + 17 = 0$
The distance of the focus from the directrix
$\begin{aligned} = |\frac{5 \times 1 - 12 \times 3 + 17}{\sqrt{5^{2} + (- 12)^{2}}}| = \frac{14}{13} \\ ∴ latus rectum = 2 \times \frac{14}{13} = \frac{28}{13} \end{aligned}$

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Parabola

Remember concepts with our Masterclasses.

If the length of the latus rectum of the parabola 169(x−1)2+(y−3)2=(5x−12y+17)2 is L then the value of 13L is

Here, (x−1)2+(y−3)2=5x−12y+1752+(−12)22∴ the focus =(1,3) and the directrix is 5x−12y+17=0The distance of the focus from the directrix =5×1−12×3+1752+(−12)2=1413∴ latus rectum =2×1413=2813

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