Question:
The eccentricity of the conic \(9x^2 - 16y^2 = 144\) is
The eccentricity of the conic \(9x^2 - 16y^2 = 144\) is
Show Hint
Hyperbola: \(e>1\) always.
Updated On: Apr 15, 2026
- 4/5
- 4/3
- 5/4
- \(\sqrt{7}\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
\[
\frac{x^2}{a^2} - \frac{y^2}{b^2} =1,\quad e=\sqrt{1+\frac{b^2}{a^2}}
\]
Step 1: Rewrite.
\[ \frac{x^2}{16} - \frac{y^2}{9} =1 \]
Step 2: Compute.
\[ e=\sqrt{1+\frac{9}{16}} = \sqrt{\frac{25}{16}} = \frac{5}{4} \]
Step 1: Rewrite.
\[ \frac{x^2}{16} - \frac{y^2}{9} =1 \]
Step 2: Compute.
\[ e=\sqrt{1+\frac{9}{16}} = \sqrt{\frac{25}{16}} = \frac{5}{4} \]
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