Integral Calculus: JEE Main 2026 Mathematics question

Let a differentiable function $f$ satisfy the equation $\int_0^{36} f\left(\frac{tx}{36}\right)dt = 4\alpha f(x)$. If $y = f(x)$ is a standard parabola passing through the points $(2, 1)$ and $(-4, \beta)$, then $\beta^\alpha$ is equal to ______.