Question

Length of the focal chord of the parabola $y^2=4ax$ at a distance $p$ from the vertex is

• A. $\frac{2a^2}{p}$
• B. $\frac{a^3}{p^2}$
• C. $\frac{4a^3}{p^2}$
• D. $\frac{p^2}{a}$

Answer 1

The correct option is C $\frac{4a^3}{p^2}$

Length of focal chord of parabola $y^2=4ax$ at a distance $p$ from vertex is Smallest length of focal chord is $4a$ and distance of vertex is $a$

So put $p=a$

$\left(A\right)\frac{2a^2}{p}=\frac{2a^2}{a}=2a\ne 4a\left(B\right)\frac{a^3}{p^2}=\frac{a^3}{a^2}=a\ne 4a\left(C\right)\frac{4a^3}{p^2}=\frac{4a^3}{a^2}=4a=4a$

Hence Length $=\frac{4a^3}{p^2}$