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

The correct option is B

$8$

Find the focal distance

Given: $y^2=16x$, whose ordinate is twice the abscissa

Comparing this equation with $y^2=4ax,4a=16$

$\Rightarrow a=\frac{16}{4}=4$

Since ordinate is $2$ times the abscissa, $y=2x$

Substituting $y=2x$ in $y^2=16x\Rightarrow {\left(2x\right)}^2=16x$

$$\begin{gathered} \Rightarrow 4x^2=16x \\ \Rightarrow 4x^2–16x=0 \\ \Rightarrow 4x(x–4)=0 \end{gathered}$$

So, $x=0$ or $x=4$

When $x=4$, focal distance : $x+a=4+4=8$

When $x=0$, focal distance : $a=4$

So, the Focal distance is $4$ or $8$.

Hence, The focal distance is $4$ or $8$, so, option (B) is the correct answer.