When solving for the c squared while trying to find the foci of an Ellipses?

Question

in the equation c^2 = a^2 - b^2, if c^2 turns out to be a negative number do u continue to working the problem with imaginary numbers or undefined. It also asks you to graph and I don't think we have learned to graph imaginary numbers if that is possible

Answer 1

You suppose that a is the greater axis(half axis) so c^2 never can be negativ

Answer 2

"a" is the semi-major axis of the ellipse and "b" is the semi-minor axis. Therefore

a ≥ b

Therefore

c² = a² - b² ≥ 0
c ≥ 0

Consequently "c" can never be negative.