A hyperbola has vertices at (2, -3) and (10, -3) and foci at (0, -3) and (12, -3). What is b squared?

1. The vertices and foci all share the y-coordinate negative 3, so the transverse axis is parallel to the x-axis. 2. The center is the midpoint of the vertices, which is (6, -3). 3. The transverse axis runs from x equal to 2 to x equal to 10, so 2a is 8 and a is 4. 4. That gives a squared equal to 16. 5. Each focus sits 6 units from the center at x equal to 6, so c is 6 and c squared is 36. 6. Rearranging c squared equals a squared plus b squared gives b squared equal to 36 minus 16. 7. So b squared is 20. 8. Answering 52 adds the two squares instead of subtracting them. 9. Answering 16 stops at a squared and never reaches b. 10. Answering 36 reports c squared, which measures the foci rather than the co-vertices. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.2 The Hyperbola_