Problem 98AE
The anvil of a hyperbola Let H be the hyperbola x2 − y2 = 1 and let S be the 2-by-2 square bisected by the asymptotes of H. Let R be the anvil-shaped region bounded by the hyperbola and the horizontal lines y = ±p (sec figure).
a. For what value of p is the area of R equal to the area of S?
b. For what value of p is the area of R twice the area of S?
Solution 98AE
Step 1:
We find the area of region R by integrating the hyperbola with respect to y from .
Equation of hyperbola in terms of y is :
Now, area is