Q97 / 160 · TS EAMCET 2022 (20 Jul Shift 2) · Mathematics

If one end of a focal chord of the parabola $y^2=\frac{8}{a} x(a>0)$ is at $(1,4)$, then the length of this focal chord is

  • A
    $\frac{25}{8}$
  • B
    $\frac{25}{2}$
  • C
    $\frac{25}{4}$
  • Correct answer
    D
    25

Solution

We have $\mathrm{y}^2=(8 / \mathrm{a}) \mathrm{x}$ Since point $(1,4)$ lies on the given curve $$ \Rightarrow \mathrm{a}=\frac{1}{2} $$ or equation will be $\mathrm{y}^2=16 \mathrm{x}$ where $\mathrm{a}^{\wedge}=4$ Let $\mathrm{y}^2=4 \mathrm{a}^` \mathrm{x}$ as Hence end points of focal chord is $(1,4)$ and $(16,-16)$ $$ \begin{aligned} \text { Now length of focal chord } & =\sqrt{(-16-4)^2+(16-1)^2} \\ & =25 \end{aligned} $$

Hence, the correct answer is option: 'D'.

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