Construct a unit circle \( x^2+y^2 = 1 \) between (0,1) and (1,0). Then construct the hyp. \( x^2-y^2 = 1\) in the same interval. You should have the ++ quadrant of a unit circle. and the upper half of an hyperbola, coincident at (0,1). Construct any line from (0,0) to the curve \( x^2-y^2 = 1\) Write the formula for the area of the triangle bounded by y=0; y=tan(theta) where theta is <pi/4, and subtended by the line from (0,0) to the hyperbola; and the hyperbolic curve, in terms of x and y. Can you construct a line from (0.5,0) to the same point on the hyperbola as y=tan(theta) which is the upper right vertex of the triangle? How close can theta be to pi/2, and what limits this? P,S, you may notice that you can't fit \( x^2-y^2 = 1\) into (0,1), (1,0); the hyp. lives 'outside' x=1; you need (0,1), (1,y).