An ellipse has its center at (1, - 2), one focus at (3, -2) and one vertex at (5, -2). Then the length of its latus rectum is:

An ellipse has center $$(1, -2)$$, one focus at $$(3, -2)$$, and one vertex at $$(5, -2)$$. Find the length of the latus rectum.

The semi-major axis $$a$$ equals the distance from the center to a vertex, which is $$a = |5 - 1| = 4$$.

The distance from the center to a focus gives $$c = |3 - 1| = 2$$.

Using $$b^2 = a^2 - c^2 = 16 - 4 = 12$$, we get $$b = 2\sqrt{3}$$.

Therefore, the length of the latus rectum is $$\frac{2b^2}{a} = \frac{2 \times 12}{4} = 6$$.

The correct answer is Option 4: 6.