Question

The equation of the hyperbola in standard form whose eccentricity is $\sqrt{2}$ and the distance between whose foci is 16 is:

• A. x² - y² = 32
• B. x² - y² = 16
• C. x² - y² = 64
• D. None of these

Answer 1

Answer: (A)

x² - y² = 32

Answer 2

Since distance between the foci is 16

⇒ 2ae = 16 ⇒ 2$\sqrt{2}$a = 16

⇒ a = $\frac{8}{\sqrt{2}} = 4\sqrt{2}$.

b = 1$\sqrt{(e^{2} - 1)} = \frac{8}{\sqrt{2}} = 4\sqrt{2}$.

∴ Hyperbola is x² - y² = 32.