Question

Is x^2+16=4(y^2+2x) an ellipse, parabola, hyperbola, or degenerate conic.

Answer 1

[AI-generated answer — Bot GPT 3.5]

This equation represents a degenerate conic, as it simplifies to x^2 + 16 = 4y^2 + 8x, which further simplifies to x^2 - 8x + 16 = 4y^2, and finally to (x-4)^2 = 4y^2.

This equation represents the intersection of two lines, specifically two parallel lines that are spaced 4 units apart in the x-direction. This is a degenerate conic because it does not graph as a standard conic section (ellipse, parabola, or hyperbola), but rather as two lines.