Question
Download Solution PDFFind the length of the latus rectum of the hyperbola 9x2 - 16y2 = 144 ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
In a hyperbola \(\rm \frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), a > b:
The length of the latus rectum is equal to \(\rm \frac{2b^2}{a}\).
Calculation:
The given equation of the hyperbola can be written as:
9x2 - 16y2 = 144
Divide by 144 on both sides, we get
\(\rm \frac{x^2}{16}-\frac{y^2}{9}=1\)
\(\rm \frac{x^2}{4^2}-\frac{y^2}{3^2}=1\)
Here, b = 3 and a = 4.
Length of the latus rectum = \(\rm \frac{2 \times 3^2}{4}\) = \(\rm \frac{9}{2}\)
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