Manipal Entrance Test 2014 Math Paper

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, ae=√a2−b2
⇒ ae=2
∴ The co-ordinates of one end point oflatusrectum are (2,

5

3

) .
The equation of tangent at that point is

x

9

+

y

3

=1, this meets the co-ordinate axes at
A (0,

9

2

) and B(3,0)
Area of Delta‌A‌O‌B=

1

2

×

9

2

×3=

27

4

Hence, the area of rhombus ABCD =4×

27

4

=27 sq units