If you draw out the graphs, you'll see that one of the diagonals of the rhombus is equal to 2b.
Further, you can obtain the points of intersection with the x-axis for the other diagonal.
For y = x^2 − b,
When y = 0, x = +√b/-√b
Hence, one diagonal of the rhombus is 2b, the other is 2√b
Area of a rhombus is given by:
(1/2) * Product of diagonals
= 0.5 * 2b * 2√b
= 2b√b = 54
=> b√b = 27
=> b = 3
The area of the rhombus formed by points of intersection of parabolas y=x^2 −b and y=−x^2 +b and their vertices is 54. Find b.
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