Let P be a variable point on the parabola \( y^2 = 2x\) and Let B and C be points on the y-axis so that the circle \((x - 1)^2 + y^2 = 1\) is inscribed in triangle PBC. Find the minimum area of triangle PBC.

Guest Nov 22, 2020

#2**+1 **

Graphically I have found the answer to be about 8

Here is my interactive graph. You can move the point P around to get different areas.

https://www.geogebra.org/classic/mw7schnm

I have not worked out how to do it algebraically yet.

Melody Nov 30, 2020