Find, by integration, the area of the region bounded by the parabola $y^2 = 4ax$ and its latus rectum.

**OR**

Find, by integration, the area of the region bounded by the curves $y^2 = 4x$ and $x^2 = 4y$.

Question

Find, by integration, the area of the region bounded by the parabola $y^2 = 4ax$ and its latus rectum.

**OR**

Find, by integration, the area of the region bounded by the curves $y^2 = 4x$ and $x^2 = 4y$.

Accepted Answer

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> [!TLDR]
> main: integrate y=2√(ax) up to the latus rectum x=a, doubled for symmetry; OR: find the intersection of y²=4x and x²=4y, integrate the difference
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> **Main part.** Parabola $y^2=4ax$; the latus rectum is the vertical chord through the focus, $x=a$. By symmetry about the $x$-axis, the enclosed area is twice the area above the axis: …

Q.Find, by integration, the area of the region bounded by the parabola $y^2 = 4ax$ and its latus rectum. OR Find, by integration, the area of the region bounded by the curves $y^2 = 4x$ and $x^2 = 4y$ .

Q.Find, by integration, the area of the region bounded by the parabola $y^2 = 4ax$ and its latus rectum. OR Find, by integration, the area of the region bounded by the curves $y^2 = 4x$ and $x^2 = 4y$ .

Q.Find, by integration, the area of the region bounded by the parabola y2=4axy^2 = 4axy2=4ax and its latus rectum. OR Find, by integration, the area of the region bounded by the curves y2=4xy^2 = 4xy2=4x and x2=4yx^2 = 4yx2=4y.

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Q.Find, by integration, the area of the region bounded by the parabola y2=4axy^2 = 4axy2=4ax and its latus rectum. OR Find, by integration, the area of the region bounded by the curves y2=4xy^2 = 4xy2=4x and x2=4yx^2 = 4yx2=4y.

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Q.Find, by integration, the area of the region bounded by the parabola $y^2 = 4ax$ and its latus rectum. OR Find, by integration, the area of the region bounded by the curves $y^2 = 4x$ and $x^2 = 4y$ .

Unlock the full solution

Q.Find, by integration, the area of the region bounded by the parabola $y^2 = 4ax$ and its latus rectum. OR Find, by integration, the area of the region bounded by the curves $y^2 = 4x$ and $x^2 = 4y$ .

Unlock the full solution