# The focal distance of a point on a parabola y^2=8x. is find it.

Solution: Comparing  $\\ y^2=8x$   With  $\\ y^2=4ax$

$\therefore 4a=8\Rightarrow a=2$

$\therefore$ Equation of directrix is  $\\x+2=0$

Let $\\(\alpha ,\beta )$ on the parabola

$\\\Rightarrow y^2=8x\\ \\\therefore \beta ^2=8\alpha \\ \\\because SP=8\\ \\ \Rightarrow PM=8\Rightarrow \alpha +2=8\\ \\\Rightarrow \alpha =6Ans$

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