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:
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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