AP EAMCET · Maths · Hyperbola
Statement I The eccentricity of the hyperbola \(9 x^2-16 y^2-72 x+96 y-144=0\) is \(5 / 4\).
Statement II The eccentricity of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) is \(\sqrt{1+\frac{b^2}{a^2}}\)
- A Statement I is true, Statement II is true; Statement II is correct explanation for Statement I.
- B Both statements are true and Statement II is not the correct explanation of Statement I.
- C Statement I is false; Statement II is true.
- D Statement I is true; Statement II is false.
Answer & Solution
Correct Answer
(A) Statement I is true, Statement II is true; Statement II is correct explanation for Statement I.
Step-by-step Solution
Detailed explanation
\(9 x^2-16 y^2-72 x+96 y-144=0\) \(\begin{aligned} & \Rightarrow 9\left(x^2-8 x\right)-16\left(y^2-6 y\right)-144=0 \\ & \Rightarrow 9\left(x^2-8 x+16\right)-16\left(y^2-6 y+9\right)-144\end{aligned}\) \(-144+144=0\)…
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