Problem 4. Evaluate J yd A where D is the region in the first quadrant that lies above the hyperbola xy = 1 and the line y = x and below the line y = 2.
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- Problem 1: A hyperbola has a vertical transverse axis of length 12 and asymptotes ofProblem 4 Form the differential equation representing the family of hyperbola having the center at the origin and the foci on x-axis.Find the equations of the normal and the tangent to the hyperbola xy + 2x - 5y-2= 0 at the point (3, 2)
- Problem 3 A woman, at a point A on the shore of a circular lake with a radius of 2 miles, wants to reach point C diametrically opposite to A on the other side of the lake in the shortest possible time (see the figure). She can walk at a speed of 4 miles / hour and row at 2 miles / hour.What should be her route to get to point C in the shortest time possible?Problem 3: The parabola given by the equation y=3x2−18x+13 has its vertex at (h,k) for: h=__________ and k=__________(a) Find and identify the traces of the quadratic surface x2 +y2 -z2 =1 and explain why the graph looks like the graph of the hyperboloid of one sheet in Table 1. (b) If we change the equation in part (a) to x2 -y2 +z2 =1 , how is the graph affected? (c) What if we change the equation in part (a) to x2 +y2 +2y- z2 =0?