Correct Answer - Option 4 : None of these
CONCEPT:
The following are the properties of a vertical ellipse \(\frac{{{x^2}}}{{{b^2}}} + \frac{{{y^2}}}{{{a^2}}} = 1\) where 0 < b < a
- Its centre is (0, 0)
- Its vertices are (0, - a) and (0, a)
- Its foci are (0, - ae) and (0, ae)
- Length of major axis is 2a
- Length of minor axis is 2b
- Equation of major axis is x = 0
- Equation of minor axis is y = 0
- Length of latus rectum is 2b2/a
- Eccentricity of ellipse is \(e = \frac{\sqrt {a^2-b^2}}{a}\)
CALCULATION:
Given: Equation of ellipse is 16x2 + y2 = 16
The given equation of ellipse can be re-written as: \(\frac{{{x^2}}}{{{1}}} + \frac{{{y^2}}}{{{16}}} = 1\)
As we can see that, the given ellipse is a vertical ellipse.
So, by comparing the given ellipse with \(\frac{{{x^2}}}{{{b^2}}} + \frac{{{y^2}}}{{{a^2}}} = 1\) we get,
⇒ a2 = 16 and b2 = 1
As we know that, for the vertical ellipse the length of the minor axis is given by 2b
So, the length of the major axis for the given ellipse is 2 ⋅ 1 = 2 units
Hence, option D is the correct answer.
