If one end of a focal chord

Question:

If one end of a focal chord $\mathrm{AB}$ of the parabola $y^{2}=8 x$ is at A $\left(\frac{1}{2},-2\right)$, then the equation of the tangent to it at B is:

  1. (1) $2 x+y-24=0$

  2. (2) $x-2 y+8=0$

  3. (3) $x+2 y+8=0$

  4. (4) $2 x-y-24=0$


Correct Option: , 2

Solution:

Let parabola $y^{2}=8 x$ at point $\left(\frac{1}{2},-2\right)$ is $\left(2 t^{2}, 4 t\right)$

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

Parameter of other end of focal chord is 2

So, coordinates of

$B$ is $(8,8)$

$\Rightarrow$ Equation of tangent

at $B$ is $8 y-4(x+8)=0$

$\Rightarrow \quad 2 y-x=8$

$\Rightarrow \quad x-2 y+8=0$

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