Question
Download Solution PDFFind the length of the major axis of the ellipse \(\frac{{{x^2}}}{16} + \frac{{{y^2}}}{{9}} = 1\) ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
The properties of a horizontal ellipse \(\frac{{{x^2}}}{a^2} + \frac{{{y^2}}}{b^2} = 1\) where 0 < b < a are as follows:
- Centre of ellipse is (0, 0)
- Vertices of ellipse are: (- a, 0) and (a, 0)
- Foci of ellipse are: (- ae, 0) and (ae, 0)
- Length of major axis is 2a
- Length of minor axis is 2b
- Eccentricity of ellipse is given by: \(e = \frac{{\sqrt{{{a^2} - {b^2}} }}}{a}\)
CALCULATION:
Given: Equation of ellipse is: \(\frac{{{x^2}}}{16} + \frac{{{y^2}}}{{9}} = 1\)
As we can see that, the given ellipse is an horizontal ellipse.
By comparing the given equation of ellipse with \(\frac{{{x^2}}}{a^2} + \frac{{{y^2}}}{b^2} = 1\) where 0 < b < a we get
⇒ a = 4 and b = 3
As we know that, the length of the major axis is given by 2a
So, the length of the major axis for the given ellipse is: 2 × 4 = 8 units
Hence, option B is the correct answer.
Last updated on Jul 1, 2025
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