Question

At what point on the curve x^2 + y^2 = 9 is the tangent line vertical?

Answer 1

x² + y² = 9 is the equation of a circle with center (0, 0) and radius 3.

This puts the vertices at (-3, 0), (3, 0), (0, -3), and (0, 3).

When is the tangent line vertical? when it passes through the x-axis.

Answer: (-3, 0), (3, 0)