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Question: The length of the latusrectum of the parabola (5x - 12y + 17)<sup>2</sup> = 169\(\left\lbrack (x - 1...

The length of the latusrectum of the parabola (5x - 12y + 17)2 = 169[(x−1)2+(y−3)2]\left\lbrack (x - 1)^{2} + (y - 3)^{2} \right\rbrack is

A

14/13

B

28/13

C

12/13

D

24/13

Answer

28/13

Explanation

Solution

Given parabola is (x-1)2 + (y-3)2 = (5x−12y+1713)2\left( \frac{5x - 12y + 17}{13} \right)^{2}

This s the form SP2 = PM2

Where S = (1, 3) = focus

5x – 12y + 17 = 0 is the directrix.

∴ Length of latusrectum = 2 x (perpendicular distance from focus to directrix)

= 2 x 1413\frac{14}{13} = 28/13.