Consider the ellipse  x29 + y25  =  1 , then which of the following is (are) TRUE?Area of parallelogram formed by tangents at end points of latus rectum is 27 sq. units.Area of the parallelogram formed by tangents at end points of latus rectum is  272  sq. units.Area of rectangle formed by vertices of end points of latus rectum is  203  sq. units.Area of parallelogram formed by end points of major & minor axis is  6√5  sq. units.

The question is asking for the truthfulness of four statements related to the ellipse defined by the equation x^2/9 + y^2/5 = 1.

1. The area of the parallelogram formed by tangents at the endpoints of the latus rectum is 27 sq. units.
2. The area of the parallelogram formed by tangents at the endpoints of the latus rectum is 272 sq. units.
3. The area of the rectangle formed by the vertices of the endpoints of the latus rectum is 203 sq. units.
4. The area of the parallelogram formed by the endpoints of the major & minor axis is 6√5 sq. units.

Let's evaluate each statement:

1. The latus rectum of an ellipse is the line segment that passes through the focus of the ellipse, is perpendicular to the major axis and both its endpoints lie on the ellipse. The length of the latus rectum of an ellipse with equation x^2/a^2 + y^2/b^2 = 1 (a>b) is 2b^2/a. In this case, a^2 = 9 and b^2 = 5, so the length of the latus rectum is 2*5/3 = 10/3. The area of the parallelogram formed by the tangents at the endpoints of the latus rectum is twice the square of the length of the latus rectum, which is not 27 sq. units. So, the first statement is FALSE.

2. Using the same reasoning as above, the area of the parallelogram formed by the tangents at the endpoints of the latus rectum is not 272 sq. units. So, the second statement is FALSE.

3. The rectangle formed by the vertices of the endpoints of the latus rectum has sides of length 2a and 2b, which are 6 and 2sqrt(5), respectively. Therefore, the area of this rectangle is 62sqrt(5) = 12sqrt(5), which is not 203 sq. units. So, the third statement is FALSE.

4. The parallelogram formed by the endpoints of the major & minor axis has sides of length 2a and 2b, which are 6 and 2sqrt(5), respectively. Therefore, the area of this parallelogram is 62sqrt(5) = 12sqrt(5), which is not 6√5 sq. units. So, the fourth statement is FALSE.

Therefore, all four statements are FALSE.