Find the minimum of $x-y$ among all ordered pairs of real numbers $(x, y)$, $x$ and $y$ between 0 and 1, where there exists a re
al number $a \neq 1$ such that \[ \log_{x}a + \log_{y}a = 4\log_{xy}a. \]
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"determine the location" or namely, is it inside the circle, outside the circle, or right ON the circle?
well, we know the center is at (1,-5) and it has a radius of 5, so the distance from the center to any point on the circle will just be 5, now if (4,-1) is less than that away, is inside, if more than that is outiside and if it's exactly 5 is right ON the circle.
well, we can check by simply getting the distance from the center to the point (4,-1).