MHT CET · Maths · Hyperbola
The eccentricity of a rectangular hyperbola is
- A 2
- B \(2 \sqrt{2}\)
- C 1
- D \(\sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{2}\)
Step-by-step Solution
Detailed explanation
equation of rectangular hyperbola
\(x^2 - y^2 = p^2 \Rightarrow \frac{x^2}{p^2} - \frac{y^2}{p^2} = 1\)
Here, length of transverse axis and conjugate axis are equal,
\(\therefore \text{Eccentricity} = \sqrt{1 + \left(\frac{b}{a}\right)^2} = \sqrt{1 + \left(\frac{p}{p}\right)^2} = \sqrt{1 + 1} = \sqrt{2}\)
\(x^2 - y^2 = p^2 \Rightarrow \frac{x^2}{p^2} - \frac{y^2}{p^2} = 1\)
Here, length of transverse axis and conjugate axis are equal,
\(\therefore \text{Eccentricity} = \sqrt{1 + \left(\frac{b}{a}\right)^2} = \sqrt{1 + \left(\frac{p}{p}\right)^2} = \sqrt{1 + 1} = \sqrt{2}\)
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