Applications Of Integrals

First of all we draw the graph,

Required area i.e., (OMPNO)

Given, In ellipse the distance between the foci = Length of the latusrectum ....(i) [from E (i)] (by quadratic formula)

Equation of parabola is and line For intersection point of both curves put , we get



Then, or
Intersection points are and

Required area
(given)


Now, if

If

We have, and
...(i)
On putting in E (i), we get

Equation of tangent at is

Required area



sq unit

In figure,
and is a square.

So, side of length units
Area of sq units