Question

The foci of the ellipse \( \frac{x^2}{144} + \frac{y^2}{81} = 1 \) and the hyperbola \( \frac{x^2}{144} - \frac{y^2}{81} = 1 \) coincide then value of \( b^2 \) is

• A. 1
• B. 5
• C. 7
• D. 9

Hint:

The foci of an ellipse and a hyperbola are related by the equation \( c^2 = a^2 \pm b^2 \).

Answer 1

The Correct Option is D

Step 1: Foci of the Ellipse and Hyperbola.
For both the ellipse and the hyperbola, the foci coincide. The relationship between \( a^2 \), \( b^2 \), and the foci for the ellipse and hyperbola is used to find \( b^2 \). Using the given equation, we find \( b^2 = 9 \).
Step 2: Conclusion.
The correct answer is (D), 9.