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Question: The area enclosed between the parabolas y<sup>2</sup> = 4ax and x<sup>2</sup> = 4by is –...

The area enclosed between the parabolas y2 = 4ax and

x2 = 4by is –

A

83\frac{8}{3}ab

B

163\frac{16}{3}ab

C

43\frac{4}{3}ab

D

None of these

Answer

163\frac{16}{3}ab

Explanation

Solution

y2 = 4ax … (1)

x2 = 4by … (2)

Using (2) in (1) x416b2\frac{x^{4}}{16b^{2}} = 4ax Ž x = 0 or x3 = 64ab2 i.e.

x = 0, 4a1/3 b2/3.

\ Required area= 4ax\sqrt{4ax}x24b\frac{x^{2}}{4b}dx

= 163\frac{16}{3}ab. (on calculation)