Geometric Approach Explained
Okay, here’s how it goes. The trick is to make the right-angled triangle in the picture. The slope of the radial line is –h/a from rise over run, and that’s equal to the slope we found on the previous page, -1/(2a), which solves to give us h = 1/2.
Since the radius is 1, we get the following from Pythagoras:
a2 = 1 - (1/2)2 = 3/4
Finally let’s locate the centre of the circle. The parabola at x = a has height y = a2 so the centre of the circle has height