Question 1142382
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The function is equivalent to xy = 25/2.<br>
Statement A: True if x positive makes y positive also and x negative makes y negative also.  Is that true about this function?<br>
Statement B: This will be easier after you look at statement C.<br>
Statement C: True if the system of equations xy=25/2 and y=x has two solutions.<br>
{{{xy = 25/2}}} --> {{{x^2 = 25/2}}} (because y=x) --> {{{x = 5/sqrt(2)}}} or {{{x = -5/sqrt(2)}}}<br>
Back to Statement B: Because the equation is symmetric in x and y (exchanging the two variables produces the same equation), the graph is symmetric about the line y=x.  That means the shortest distance from the origin to a point on the graph is the distance to one of the two points found in working on Statement C.  A simple application of the distance formula will give you that distance.