Question

The length of the latusrectum of the parabola $169\{{(x-1)}^2+{(y-3)}^2\}={(5x-12y+17)}^2$

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

Answer 1

The correct option is B $\frac{28}{13}$

Here ${(x-1)}^2+{(y-3)}^2={\left\{\frac{5x-12y+17}{\sqrt{5^2+{(-12)}^2}}\right\}}^2$

$\therefore$ The focus is $(1,3)$ and the directrix is $5x-12y+17=0$

The distance of the focus from the directrix

$=\left|\frac{5\times 1-12\times 3+17}{\sqrt{5^2+{(-12)}^2}}\right|=\frac{14}{13}$

$\therefore$ Length of latusrectum $=2\times \frac{14}{13}=\frac{28}{13}$