Question

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

• A. $\frac{14}{11}$
• B. $\frac{12}{13}$
• C. $\frac{28}{13}$
• D. none of these

Answer 1

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

Given parabola may be written as, $(x-1{)}^2+(y-3{)}^2={\left(\frac{5x-12y+17}{\sqrt{5^2+{12}^2}}\right)}^2$

Thus focus of the parabola is $(1,3)$ and directrix is $5x-12y+17$

Now distance between directrix to the focus is $=\frac{5\left(1\right)-12\left(3\right)+17}{\sqrt{5^2+{12}^2}}=\frac{14}{13}$

Hence length of latus rectum of the parabola is $=2\times \frac{14}{13}=\frac{28}{13}$