Question

Consider the following with regard to eccentricity (e) of a conic section:

1. e = 0 for circle

2. e = 1 for parabola

3. e < 1 for ellipse

Which of the above statements is/are correct?

1. 1 and 2 only
2. 2 and 3 only
3. 1 and 3 only
4. 1, 2 and 3

Answer 1

Correct Answer - Option 4 : 1, 2 and 3

CONCEPT:

Eccentricity:

The constant ratio of distance of point lying on conic from the focus to its perpendicular distance from directrix is called the eccentricity of a conic section and is denoted by e.

• For an ellipse: e < 1
• For a parabola: e = 1
• For a hyperbola: e > 1
• For a circle: e = 0
• For a pair of straight lines: e = ∞

CALCULATION:

As we know that, eccentricity of a circle is 0 i.e e = 0 for a circle.

So, statement 1 is correct.

We also know that, eccentricity of a parabola is equal to 1 i.e e = 1 for a parabola.

So, statement 2 is also correct.

We also know that, eccentricity of an ellipse is always less than 1 i.e e < 1 for an ellipse.

So, statement 3 is also correct.

Hence, correct option is 4.