Question

The base of S is an elliptical region with the boundary curve 9x²+4y²=36. Cross-sections perpendicular to the x-axis are:

a) Rectangles
b) Isosceles right triangles
c) Parallelograms
d) Circles

Answer 1

The cross-sections perpendicular to the x-axis of the given elliptical region with the boundary curve 9x²+4y²=36 are isosceles right triangles.

Step-by-step explanation:

An ellipse is a closed curve wherein the distances from the two foci to any point on the curve are equal. In this case, the boundary curve of the elliptical region is given by the equation 9x²+4y²=36. To determine the cross-sections perpendicular to the x-axis, we need to find the equation of the line that represents the intersection of the elliptical region with the plane perpendicular to the x-axis. By taking slices at different values of x, we can observe that the cross-sections are isosceles right triangles.