Limit SMT Intermediate

Problem - 4574

Consider the parabola $y=ax^2 + 2019x + 2019$. There exists exactly one circle which is centered on the $x$-axis and is tangent to the parabola at exactly two points. It turns out that one of these tangent points is $(0, 2019)$. Find $a$.

The solution for this problem is available for $0.99.
You can also purchase a pass for all available solutions for $99.