let's intersect them:
x^2 - b = -x^2 + b
2x^2 = 2b
x = ± √b
then y = 0
So the points of intersection are (√b,0) and (-√b,0)
Their vertices are (0,b) and (0,-b)
Which makes the lengths of their diagonals equal to 2b and 2√3
Since the area of a rhombus is the product of their diagonals/2
we have:
2b(2√3)/2 = 54
I will let you finish it.
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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