Examples: Find the area bounded by the parabola `y^2 = 4ax` and its latus rectum.

Explanation

Here, the parabolic equation is `y^{2}=4 a x`

Let O be the vertex, S be the focus and LL' be the latus rectum of the given parabola.

So, latus rectum is `x=a.`

Also, It is known that parabola is symmetric about x – axis.

So, Required area `=2( area of OSL )`

So, Required area
`=2 int_{0}^{2} y d x= 2 int_{0}^{a} 2 sqrt{a} sqrt{x} d x`

`=2 cdot 2 sqrt{a} int_{0}^{2} x^{frac{1}{2}} d x=4 sqrt{a}[frac{x^{3}}{frac{3}{2}}]_{0}^{2}`

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