Page 167 - Excel for Scientists and Engineers: Numerical Methods

144 EXCEL: NUMERICAL METHODS

4. An ellipse is a plane figure described by the locus of a point P(x, y) that
moves such that the sum of its distances from two fixed points (foci) is a
constant. If the ellipse has foci located at A (-c, 0) and B (c, 0) and the
distance ACB is 2a, then by setting b = J n , the equation of the ellipse

is simplified to

x2 y2
-+-=1
a2 b2
(a and b are termed the semiaxes of the ellipse).
1T

I I
-1.5 1.5

Figure 7-17. Approximating the circumference of an ellipse.
For the ellipse shown in Figure 7-17, with foci at x = -0.5, y = 0 and x = 0.5,
y = 0 and a = 1, determine the circumference of the ellipse.

5. Determine the area of the ellipse of problem 7-4.

6. Find the area between the curve y = 2x - x2 and the line y = -3.

7. Find the area between the curve y = 2x - x2 and the line y = 2.5~ 2.3
-

8. Find the area enclosed between the two curves shown in Figure 7-7: y1 = x3 -
20x2 - lOOx + 2000 andy2 = 2x3 - 5x2 - 300x + 1000. The curves intersect in
the region between x = -5 and x = 15.

9. The area between the curve y = x2 and the horizontal line y = 4 is divided into
two equal areas by the horizontal line y = c. Find c.