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

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Aicharya · Accepted Answer

Given parabola, $\begin{array}{cc} & 169\left[(x-1)^2+(y-3)^2\right]=(5 x-12 y+17)^2 \ \Rightarrow & (x-1)^2+(y-3)^2=\left(\frac{5 x-12 y+17}{13}\right)^2 \ \Rightarrow & (S P=P M) \end{array}$ Here, focus is $S(1,3)$ and directrix $(5 x-12 y+17)=0$ $\therefore$ Distance of focus from directrix $\begin{aligned} & \Rightarrow \quad 2 a=\left|\frac{5-36+17}{\sqrt{25+144}}\right| \ & \Rightarrow \quad 2 a=\frac{14}{13} \ & \therefore \text { Latusrectum }=4 a=\frac{28}{13} \end{aligned}$

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

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