Question

The eccentricity of the parabola is :

• A. 1
• B. 0
• C. Less than 1
• D. Greater than 1

Hint:

Memorize the eccentricity values of all conic sections:
- Circle: \(e = 0\)
- Ellipse: \(e < 1\)
- Parabola: \(e = 1\)
- Hyperbola: \(e > 1\)

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The eccentricity (\(e\)) is a key parameter that characterizes the shape of a conic section.
It is defined as the constant ratio of the distance of any point on the conic from a fixed point (called the focus) to its perpendicular distance from a fixed straight line (called the directrix).

Step 2: Detailed Explanation:
The conic sections are classified based on the value of their eccentricity \(e\):
1. Parabola: By definition, a parabola is the locus of a point whose distance from the focus is exactly equal to its distance from the directrix.
Therefore, the ratio of these distances is:
\[ e = \frac{\text{Distance from Focus}}{\text{Distance from Directrix}} = 1 \]
Thus, the eccentricity of a parabola is always exactly equal to 1. This makes Option (A) correct.
Let us review the eccentricities of other conic sections:
- Circle: The eccentricity of a circle is 0 (Option B).
- Ellipse: The eccentricity of an ellipse is strictly less than 1 (Option C), i.e., \(0 < e < 1\).
- Hyperbola: The eccentricity of a hyperbola is strictly greater than 1 (Option D), i.e., \(e > 1\).
Thus, only Option (A) is correct.

Step 3: Final Answer:
The correct option is (A).