If one end of a focal chord of the parabola,

Question:

If one end of a focal chord of the parabola, $y^{2}=16 x$ is at $(1,4)$, then the length of this focal chord is:

  1. (1) 25

  2. (2) 22

  3. (3) 24

  4. (4) 20


Correct Option: 1

Solution:

$\because y^{2}=16 x$

$\Rightarrow a=4$

One end of focal of the parabola is at $(1,4)$

$\because \mathrm{y}$ - coordinate of focal chord is $2 a t$

$\therefore 2 a t=4$

$\Rightarrow t=\frac{1}{2}$

Hence, the required length of focal chord

$=a\left(t+\frac{1}{t}\right)^{2}=4 \times\left(2+\frac{1}{2}\right)^{2}=25$

 

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