Calculating Beta distribution parameters (alpha, beta) using Cumulative Density Function (CDF)

Hi all,
I am trying to find Beta distribution parameters (alpha, beta) from CDF curve that goes through two points.

Let's say points are (x1,p1) & (x2,p2) where x1,x2 represent points on x-axis; and p1,p2 represent probability points on y-axis.
Instead of x-axis scale (0-1); I am using a scale of 1-100.

To be more specific, for instance, if the points are (10, 0.1) & (80, 0.7); how can I find the values of alpha & beta for Beta distribution using CDF.

Your help is much appreciated.