Question

Find the area of the largest rectangle with sides parallel to the coordinate axes which can be inscribed bounded by x²=2y-4 and x² = y-4.

Answer 1

To find the area of the largest rectangle inscribed between the curves, you need to find the points of intersection and calculate the length and width of the rectangle.

Step-by-step explanation:

To find the area of the largest rectangle inscribed between the curves:

1. Start by finding the points at which the curves intersect. Set the equations equal to each other and solve for x: x² = 2y - 4 and x² = y - 4.
2. This will give you two x-values.
3. Substitute these values back into either equation to find the corresponding y-values.
4. Now you have the coordinates of the points of intersection: (x1, y1) and (x2, y2).
5. The length of the rectangle will be the difference between the x-values: l = x2 - x1.
6. The width of the rectangle will be the difference between the y-values: w = y2 - y1.
7. The area of the rectangle is then A = l * w.