Question

The length of the latus rectum of the parabola $169\left[(x-1)^{2}+(y-3)^{2}\right]=(5 x-12 y+ 17) ^{2}$ is:

• A. $\frac{14}{13}$
• B. $\frac{12}{13}$
• C. $\frac{28}{13}$
• D. None of these

Answer 1

Answer: (C)

$\frac{28}{13}$

Answer 2

Given equation can be rewritten as
$(x-1)^{2}+(y-3)^{2}=\left(\frac{5 x-12 y+17}{13}\right)^{2}$
$\Rightarrow \quad S P=P M$
Here, focus is $(1,3)$, directrix
$5 x-12 y+17=0$
$\therefore$ the distance of the focus from the directrix
$=\left|\frac{5-36+17}{\sqrt{25+144}}\right|$
$=\frac{14}{13}=2 a$
$\therefore$ Latusrectum $=2 \times \frac{14}{13}=\frac{28}{13}$