Question

If $t$ is the parameter for one end of a focal chord of the parabola $y^2 = 4ax$, then its length is

• A. $a\left(t+\frac{1}{t}\right)^2$
• B. $a\left(t-\frac{1}{t}\right)^2$
• C. $a\left(t+\frac{1}{t}\right)$
• D. $a\left(t-\frac{1}{t}\right)$

Answer 1

Answer: (A)

$a\left(t+\frac{1}{t}\right)^2$

Answer 2

If $t, t'$ are the ends of the focal chord of parabola $y^{2}= 4ax$, then its length $= a\left(t'-t\right)^{2}$ But for a focal chord $tt' =-1$ $\therefore t' = -\frac{1}{t}$ $\therefore$ reqd. length $= a\left(-\frac{1}{t} -t\right)^{2}$ $= a\left(t+\frac{1}{t}\right)^{2}$