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)

$8$

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 is

$\sqrt{(4-4{)}^2+(8-0{)}^2}=8$