In an ellipse, distance from the center to one of the vertex $(v_1)$ is $a$; center to one of the co-vertex is $b$ and $c$ is the distance from the center to the focus that is close to the vertex $(v_1)$.
The textbook goes on to say the square of $a$ is equal to the sum of the squares of $b$ and $c$. How can that be? The sum of the squares of $b$ and $c$ will be the square of the line connecting the outer edge of the $c$ to the outer edge of the $b$ (co-vertex), is it not? Otherwise, it will be violating the Pythagoras theorem. What am I missing?
I am familiar with Cauchy-Schwarz inequality. But how does that explain $a^2=b^2 + c^2$? Thanks for your help!
the SQUARE ROOT OF THE sum of the squares of b and c is one line. "a" is another line. They happen to be equal in length.