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# The smallest distance between the origin and a point on the graph of can be expressed as , where a and b are positive integers

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The smallest distance between the origin and a point on the graph $$y=\frac{1}{\sqrt{2}}\left(x^2-3\right)$$ of  can be expressed as $$\sqrt{a}/b$$, where a and b are positive integers such that a is not divisible by the square of any integer greater than one. Find a+b.

I tried just finding the zeros of the function but that was wrong. If someone could get me started but not give me the answer I would apreciate it.

Jun 1, 2019

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If (x, y) is a point on the graph its distance from the origin will be sqrt(x^2 + y^2),

and it's this you have to find the minimum value of.

However, since x^2 + y^2 will get you the same point it's easier if you use this.

Use the equation of the curve to substitute for y^2.

Jun 1, 2019