The image contains a list of conic section equations, and the task is to identify the type of conic section based on the equations. Let's break down and identify each equation:

1. $(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1$
   This represents an ellipse, where $a^2$ and $b^2$ are the squared lengths of the semi-major and semi-minor axes.

2. $(x-h)^2 / a^2 - (y-k)^2 / b^2 = 1$
   This represents a hyperbola, where $a^2$ and $b^2$ determine the distances from the center along the x and y axes, respectively.

3. $(x-h)^2 + (y-k)^2 = r^2$
   This is a circle, with center $(h, k)$ and radius $r$.

4. $(x-h)^2 + (y-k)^2 = r^2$ where $r = 0$
   This represents a degenerate circle, which reduces to a point at $(h, k)$ because the radius is zero.

5. $(y-k)^2 / a^2 = 1$
   This is a degenerate parabola or could represent two parallel lines.

6. $(x-h)^2 / a^2 - (y-k)^2 / b^2 = 0$
   This represents a degenerate hyperbola, which is a pair of intersecting lines.

7. $(x-h)^2 / a^2 - (y-k)^2 / b^2 = -1$
   This is an imaginary hyperbola, meaning there are no real solutions because the right-hand side is negative.

8. $(y-k)^2 = 4a(x-h)$
   This is a parabola that opens horizontally, where $a$ determines the distance from the vertex to the focus.

9. $(x-h)^2 + (y-k)^2 = r^2$ where $r < 0$
   This is an imaginary circle, because a negative radius isn't possible in real geometry.

10. $(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1$ where $a = 0$
    This is a degenerate ellipse that collapses to a line.

Would you like more detailed explanations on any of these equations?

Here are 5 related questions to expand this:

1. What conditions define a degenerate conic section?
2. How can you distinguish between ellipses and hyperbolas based on their general equations?
3. What role do the constants $a$ and $b$ play in conic section equations?
4. How do imaginary solutions arise in conic sections, and what do they represent geometrically?
5. Can a parabola be classified as a degenerate form under certain conditions?

Tip: For conic sections, remember that if the sum of squared terms equals a positive constant, it's either a circle or ellipse. If it's a difference, it's a hyperbola.