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Q.
Find the length of latus rectum of the parabola $y^{2} = 8x$.
Conic Sections
Solution:
The given parabola is, $y ^{2}+8 x -2 y +17=0$
$
\begin{array}{l}
\Rightarrow\left( y ^{2}-2 y +1\right)=-8 x -17+1=-8 x -16 \\
\Rightarrow( y -1)^{2}=-8( x +2)
\end{array}
$
Comparing with standard parabola $Y ^{2}=-4 a X$
$
Y = y -1, X = x +2, a =2
$
Hence length of latus rectum is $=4 a=4 \times 2=8$