Question:
The foci of the hyperbola $\frac{x^2}{\cos^2 \alpha} - \frac{y^2}{\sin^2 \alpha} = 1$ are
The foci of the hyperbola $\frac{x^2}{\cos^2 \alpha} - \frac{y^2}{\sin^2 \alpha} = 1$ are
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Use $\sin^2\theta + \cos^2\theta = 1$ instantly in such problems.
Updated On: Apr 30, 2026
- $(\pm1,0)$
- $(\pm a,0)$
- $(0,\pm1)$
- $(0,\pm a)$
- $(1,\pm a)$
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The Correct Option is A
Solution and Explanation
Concept:
For hyperbola:
\[
c^2 = a^2 + b^2, \text{Foci } (\pm c,0)
\]
Step 1: Identify values.
\[ a^2 = \cos^2\alpha, b^2 = \sin^2\alpha \]
Step 2: Compute $c^2$.
\[ c^2 = \cos^2\alpha + \sin^2\alpha = 1 \] \[ c = 1 \]
Step 3: Write foci.
\[ (\pm1,0) \] \[ \boxed{(\pm1,0)} \]
Step 1: Identify values.
\[ a^2 = \cos^2\alpha, b^2 = \sin^2\alpha \]
Step 2: Compute $c^2$.
\[ c^2 = \cos^2\alpha + \sin^2\alpha = 1 \] \[ c = 1 \]
Step 3: Write foci.
\[ (\pm1,0) \] \[ \boxed{(\pm1,0)} \]
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