Question

1. Area enclosed in the curves y2 = 4x and the line
x = 2y ?​

Answer 1

Step-by-step explanation:

The parabola is

${y}^{2} = 4ax \\ 4x = 4ax \\ a = 1$

Given line is 2y=x.

We can write it in the form of y=mx.

2y=x

y=(1/2)x=mx

So, m=1/2.

Now, the area is

$area = \frac{8}{3} \frac{ {a}^{2} }{ {m}^{3} } = \frac{8}{3} \frac{ {1}^{2} }{ {( \frac{1}{2} )}^{3} } \\ = \frac{8}{3} \times \frac{1}{ (\frac{1}{8} )} = \frac{8}{3} \times 8 = \frac{64}{3}$

The area is 64/3 square units.

This is a shortcut instead of integration.

You can cross check with integration.

Thank you