The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latus ractum to the ellipse x 2 9 + y 2 5 = 1 , is

Step-by-step solution

x 2 9 + y 2 5 = 1 e = 1 - 5 9 = 2 3 a 2 = 9 ,   b 2 = 5 Foci = ± ae , 0 = ± 2 , 0 Ends of latus rectum = ± ae , ± b 2 a = ± 2 , ± 5 3 Tangent at ' L ' is T = 0 2 × x 9 + 5 3 × y 5 = 1 It cuts coordinate axes at P 9 2 , 0   &   Q 0 , 3 Area of quadrilateral P Q R S = 4 (Area of triangle O P Q ) = 4  1 2 × 9 2 × 3 = 2 7 sq. units