Find the area bounded by the curve x 2 = 4y and the line x = 4y – 2.

Question

Philoid · Accepted Answer

It is given that the area of the region bounded by the parabola x² = 4y and x = 4y - 2.

Let A and B be the points of intersection of the line and parabola.

Coordinates of point A are

Coordinates of point B are (2, 1).

Now, draw AL and BM perpendicular to x axis.

We can see that

Area OBAO = Area OBCO + Area OAC) …(1)

Now, Area OBCA = Area OMBC – Area of OMBO

.

Similarly,

Area OACO = Area OLAC – Area of OLAO

Therefore, the required area is