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)

If $t,t^{\prime }$ are the ends of the focal chord of parabola $y^2=4ax$, then its length $=a{\left(t^{\prime }-t\right)}^2$
But for a focal chord $t{t}^{\prime }=-1$
$\therefore t^{\prime }=-\frac{1}{t}$
$\therefore$ reqd. length $=a{\left(-\frac{1}{t}-t\right)}^2$
$=a{\left(t+\frac{1}{t}\right)}^2$