alleryStart learning →A plane that passes through the apex of the double cone produces which kind of result?
AAn ellipse or a circle only
BA parabola in every case
CA hyperbola in every case
DA point, a line, or two lines
Answer & Solution
Correct answer: D. A point, a line, or two lines
1. A cut that misses the apex gives one of the four ordinary conics.
2. A cut through the apex collapses the curve into a degenerate case.
3. The three degenerate results are a point, a single line, or two intersecting lines.
4. An ellipse cannot appear here because the apex forces the cross-section to pinch shut.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.4 Rotation of Axes_
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