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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