Trying to find the minimum graphically in a constrained function

Question

Using GeoGebra i get this:

The blue circle is f, and everything that is inside the yellow zone is the feasible region.

Things is if i were to draw the feasible region in paper i would never conclude that point (3.35,3.52) is the minimum, i would rather assume point (6,0). Even chatgpt doesnt guess the right point unless i mention it.

How would you guys solve this graphically without any assistance tool?

Answer 1

Hint.

Here $f(x,y) = x^2+(y-1)^2$ and the black circles represent the level curves for $f$. The feasible region is represented in light blue. As can be observed, the level curve which is tangent (minimum distance) to the feasible region is draw as dashed red. The exact tangent point can be obtained by solving:

Determine $r$ such that

$$ \cases{x^2+(y-1)^2 = r^2\\ 4x+3y = 24} $$

are tangent.