Question

Find the area of the region included between the parabolas y² = 4ax and x² = 4ay, where a > 0.

Answer 1

Given parabolas are y² = 4ax .....(i),  x² = 4ay ...(ii)

Obviously, curve (i) is right handed parabola having vertex at (0, 0), while curve (ii) is upward parabols having vertex at (0, 0).

Shaded region is required region.

For coordinate of intersection point A, (i) and (ii) are solved as

Hence, coordinate of A ≡ (4a, 4a)

Therefore, area of required region = area of OCABO - area of ODABO

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