Category Archives: Calculus

Four points $A$, $B$, $C$ and $D$ are chosen on each of $4$ hyperbola branches of $x^2y^2=1$ (as $y=\dfrac{1}{x}$ and $y=-\dfrac{1}{x}$ combined). Find the minimum area of the quadrilateral.🔑 Solution: Given that all 4 vertices of the quadrilaterial are on the $4$ branches, let … Continue reading →

$x^2y^2=1$ forms $4$ hyperbola branches, as $y=\dfrac{1}{x}$ and $y=-\dfrac{1}{x}$ combined. What is the smallest triangle in terms of area that it intersects all $4$ branches.🔑 Solution: Obviously, to be the smallest triangle, the vertices of the triangle must be on … Continue reading →