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The line segment which passes though a focus, is perpendicular to the major axis, and has its endpoints on the ellipse is called a latus rectum.

• Find the length of a latus rectum of the ellipse [math]4x^2 + 9y^2 = 36[/math].
• Find the length of a latus rectum of the ellipse [math]b^2x^2 + a^2y^2 = a^2b^2[/math]. (Assume that [math]b \lt a[/math].)
• Show that both latera recta of an ellipse are the same length.