Chapter 8.4, Problem 60E

Solution

To identify which one is not a reason to rotate the axes of a conic.

C. To place the center or vertex at the origin.

When the axes of a conic are rotated, it changes the coordinates axes and simplify the equation of a conic by eliminating the cross-product term, helps in identifying the conic and makes easier to graph the conic by hand by revealing key features.

The rotation of the axes does not shift the center or the vertex of the conic to origin.

Therefore, the reason for which a conic is not rotated is “to place the center or vertex at the origin”.

Conclusion:

The correct option is C. to place the center or vertex at the origin.