Find the point on the curve `y^2=2x` which is at a minimum distance from the point `(1,\ 4)` .

Explanation

The given equation of curve is `y^{2}=2 x` and the given point is `Q(1,4)`.

Let `P(x, y)` be the point, which is at a minimum distance from point `Q(1,4)`

Now, distance between points `P` and `Q` is given by

`P Q=sqrt{(1-x)^{2}+(4-y)^{2}} `

{ using distance formula }

`d=sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}`


or `P Q =sqrt{1+x^{2}-2 x+16+y^{2}-8 y} `

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