Question

The focal distance of a point on the parabola $ y^2 = 16x $ whose ordinate is twice the abscissa, is

• A. $ 6 $
• B. $ 8 $
• C. $ 10 $
• D. $ 12 $

Answer 1

Answer: (B)

Given curve is $y^{2}=16 x$. Let the point be $(h, k)$ But $2 h=k$, then $k^{2}=16 h$
$\Rightarrow \,\,\, 4 h^{2}=16 h$
$\Rightarrow \,\,\, h=0,\,\, h=4$
$\Rightarrow \,\,\, k=0, \,\,k=8$
$\therefore $ Points are $(0,0),(4,8) $
Hence, focal distance are respectively
$0+4=4,4+4=8$
$(\because$ focal distance $=h-a)$