Question
Download Solution PDFFind the length of the minor axis of the ellipse 4x2 + 9y2 = 144 ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
The following are the properties of a horizontal ellipse
- Its centre is (0, 0)
- Its vertices are (- a, 0) and (a, 0)
- Its foci are (- ae, 0) and (ae, 0)
- Length of the major axis is 2a
- Length of the minor axis is 2b
- Equation of major axis is y = 0
- Equation of minor axis is x = 0
- Length of the latus rectum is given by
- Eccentricity is given by
CALCULATION:
Given: Equation of ellipse is 4x2 + 9y2 = 144
The given equation of ellipse can be re-written as
As we can see that, the given ellipse is a horizontal ellipse.
So, by comparing the given equation of an ellipse with
⇒ a2 = 36 and b2 = 16
⇒ b = 4
As we know, the length of the minor axis of an ellipse is given by 2b
So, the length of the minor axis is 2 × 4 = 8 units
Hence, option B is the correct answer.
Last updated on Jul 1, 2025
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