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