Find a Cartesian equation in standard form for the ellipse with center at , semi-axes of lengths 4 and 3, and major axis parallel to the -axis.

Since the major axis has length 4 and is parallel to the -axis we have , and since the minor axis has length 3 we have . Since the center is at we then have the Cartesian equation

I believe the length of the length of the two axis would be equal to 2b and 2a respectively, not just a and b, but someone let me know if I’m wrong

You are right, that’s why exercise 13.24.10 has the solution given in the book. a and b alone are semiaxes.