Which curve represents the locus of points where the distance from a fixed point bears a constant ratio greater than one to its distance from a fixed directrix_______________?
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Answer: B. hyperbola
Explanation
A hyperbola is defined as the locus of points where the distance ratio to a fixed point and directrix is constant and greater than one. Conic section geometry classifies curves based on the eccentricity value, where a hyperbola strictly requires eccentricity greater than unity. The constant ratio between the distance from the focus and the distance from the directrix mathematically generates two open hyperbolic branches. Eccentricity is the key parameter defining conic sections, separating ellipses, parabolas, and hyperbolas mathematically. A hyperbola features two asymptotes and is formed when a plane intersects both halves of a double right circular cone. The difference in distances from any point on a hyperbola to two fixed foci remains constant throughout the curve.
An ellipse has an eccentricity strictly less than one, where the distance ratio from a focus to directrix is less than unity. A parabola has an eccentricity equal to exactly one, representing the boundary transition between ellipses and hyperbolas. A circle is a special case of an ellipse where the eccentricity is zero and the directrix is located at infinity.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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