We know that the major axis of the ellipse is 12 ( 2 a = 12 ).An ellipse is a curve with 2 focal points, such that the sum of the distances to the 2 focal points is constant for every point on a curve.If P is a point on a curve:PF 1 + PF 2 = 2 a( Blue line ) + ( Red line ) = 2 a = 12Answer: The sum of the lengths of the red and blue line segments is 12.