The area of the quadrilateral formed by the tangents at the end point of latusrectum to the ellipse x^2 9 + y^2 5 =1 is

Step-by-step solution

The quadrilateral formed by the tangents at the end points of the latusrectum is a rhombus. It is symmetrical about the axes. So, total area is four times the area of the right triangle formed by the tangents and the axes in the first quadrant. Now, aligned & a e= a^2-b^2 & a e=2 aligned The co-ordinates of one end point latusrectum are (2, 5 3 ) . The equation of tangent at that point is x 9 2 + y 3 =1 , this meets the co-ordinate axes at A (0, 9 2 ) and B(3,0) . Area of A O B= 1 2 9 2 3= 27 4 Hence, the area of r