Search any question & find its solution
Question:
Answered & Verified by Expert
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
Options:
Solution:
1019 Upvotes
Verified Answer
The correct answer is:
\(\frac{28}{13}\)
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
\(\begin{aligned}
& \Rightarrow \quad 2 a=\left|\frac{5-36+17}{\sqrt{25+144}}\right| \\
& \Rightarrow \quad 2 a=\frac{14}{13} \\
& \therefore \text { Latusrectum }=4 a=\frac{28}{13}
\end{aligned}\)
\(\begin{array}{cc}
& 169\left[(x-1)^2+(y-3)^2\right]=(5 x-12 y+17)^2 \\
\Rightarrow & (x-1)^2+(y-3)^2=\left(\frac{5 x-12 y+17}{13}\right)^2 \\
\Rightarrow & (S P=P M)
\end{array}\)
Here, focus is \(S(1,3)\) and directrix \((5 x-12 y+17)=0\)
\(\therefore\) Distance of focus from directrix
\(\begin{aligned}
& \Rightarrow \quad 2 a=\left|\frac{5-36+17}{\sqrt{25+144}}\right| \\
& \Rightarrow \quad 2 a=\frac{14}{13} \\
& \therefore \text { Latusrectum }=4 a=\frac{28}{13}
\end{aligned}\)
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.