Question on Parabola and Area Covered by Parabola

A parabola is a geometrical figure which is expressed in terms of cartesian system. In the same problem you will learn how to find area covered by parabolas.

Topic : Parabola and Area covered by two parabola

In the problem area covered will be one among the choice given.

Question : Find the area covered by two parabola y² = 4ax and x² = 4ay
(a). 16a²/3
(b). 5a²
Solution :
Choice a is correct
The equations of the given parabolas are
y² = 4ax -------- (1) and
x² = 4ay -------- (2)


The vertices of these parabolas are at the origin and their axes are x-axis and y-axis respectively as shown in figure.

















Solving (1) and (2) for x and y, we get
x⁴
----- = 4ax
16a²
=> x(x³ - 64a³) = 0
=> x = 0, x = 4a
when x = 0, y =0
And when x=4a, y=4a
The points of intersection of two parabolas are (0,0) and (4a,4a).
Therefore required area (common to both the parabolas)
















^{Choice b is incorrect}