MP Board · Class 11 · Mathematics · Conic SectionsThe foci of the hyperbola $\frac{x^2}{16} - \frac{y^2}{9} = 1$ are:
Step-by-Step Solution
For the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, $a^2 = 16$ and $b^2 = 9$. The eccentricity $e = \sqrt{1 + \frac{b^2}{a^2}} = \sqrt{1 + \frac{9}{16}} = \frac{5}{4}$. The foci are given by $(\pm ae, 0)$. Here $ae = 4 \times \frac{5}{4} = 5$. Thus, the foci are $(\pm 5, 0)$.
Detailed Options Breakdown
Option : $(\pm 5, 0)$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: $(0, \pm 5)$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Conic Sections.
Option 2: $(\pm 4, 0)$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Conic Sections.
Option 3: $(0, \pm 4)$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Conic Sections.
💡 Study Guide: This question tests core syllabus concepts from Conic Sections. For formulas, key summaries, and mock exam reference guides, read the full Conic Sections Revision Notes.