Question

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

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

Answer 1

The correct option is A $a{(t+\frac{1}{t})}^2$

R.E.F image

$y^2=4ax$

We know that

$t_1{t}_2=-1...\left(1\right)$

From the figure

$AB=AS+BS$

$=a{t}_1^2+a+a{t}_2^2+a$

$=a(t_1^2+t_2^2+2)$

$=a(t_1^2+\frac{1}{t_1^2}+2)$ [from 1]

$=a{(t_1+\frac{1}{t_1})}^2$