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The focal distance of a point on the parabola $y^{2}=16 x$ whose ordinate is twice the abscissa, is
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Verified Answer
The correct answer is:
8
Given curve is $y^{2}=16 x$. Let the point be $(h, k)$. But $2 h=k$, then $k^{2}=16 h$
$$
\begin{aligned}
\Rightarrow & & 4 h^{2} &=16 h \\
\Rightarrow & & h &=0, h=4 \\
\Rightarrow & & k &=0, k=8
\end{aligned}
$$
$\therefore$ Points are $(0,0),(4,8)$.
Hence, focal distance are respectively
$$
0+4=4,4+4=8
$$
$(\because$ focal distance $=h-a)$
$$
\begin{aligned}
\Rightarrow & & 4 h^{2} &=16 h \\
\Rightarrow & & h &=0, h=4 \\
\Rightarrow & & k &=0, k=8
\end{aligned}
$$
$\therefore$ Points are $(0,0),(4,8)$.
Hence, focal distance are respectively
$$
0+4=4,4+4=8
$$
$(\because$ focal distance $=h-a)$
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