#### notes

Take a point P at one end of the major axis.

Sum of the distances of the point P to the foci is

`F_1 P + F_2P = F_1O + OP + F_2P` (Since, ` F_1P = F_1O + OP`) = c + a + a – c = 2a

Take a point Q at one end of the minor axis.

Sum of the distances from the point Q to the foci is

`F_1Q + F_2Q = sqrt(b^2+c^2) + sqrt(b^2+c^2) = 2sqrt(b^2+c^2)`

Since both P and Q lies on the ellipse.

By the definition of ellipse, we have

`2 sqrt(b^2+c^2) = 2a , i.e., a = sqrt(b^2+c^2)`

or `a^2 = b^2 +c^2 , i.e., c = sqrt(a^2 - b^2)`