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Question

Find the coordinates of the points on the parabola $$y^2=2x$$ whose focal distance is $$\displaystyle\frac{5}{2}$$.


Solution

Comparing above parabola with $$y^2=4ax$$, we get $$a=\dfrac{1}{2}$$
So focal distance is given by, $$x+a=\dfrac{5}{2}$$ (given )
$$\Rightarrow x+\dfrac{1}{2}=\dfrac{5}{2}\Rightarrow x=2$$
Substitute $$x=2$$ in the given parabola,
$$y^2=2x=2^2\Rightarrow y=\pm 2$$

Hence coordinate of the points on the parabola whose focal distance is $$\dfrac{5}{2}$$ units are $$(2,2)$$ and $$(2,-2)$$

Mathematics

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