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Let

a, b, c

be real numbers such that

a \neq 0

. Consider the parabola with equation

y = ax^2 + bx + c,

and the lines defined by the six equations \begin{align*} &y = ax + b, & y = bx + c, \qquad & y = cx + a, \\ &y = bx + a, & y = cx + b, \qquad & y = ax + c. \end{align*} Suppose that the parabola intersects each of these lines in at most one point. Determine the maximum and minimum possible values of

\frac{c}{a}

A1

Problems(1)