Question

The differential equation $\frac{dx}{dy} = \frac{3y}{2x}$ represents a family of hyperbola (except when it represents a pair of lines) with eccentricity.

• A. $\sqrt{\frac{3}{5}}$
• B. $\sqrt{\frac{5}{3}}$
• C. $\sqrt{\frac{2}{5}}$
• D. $\sqrt{\frac{5}{2}}$

Answer 1

Answer: (D)

$\sqrt{\frac{5}{2}}$

Answer 2

$\mathbf{x}^{\mathbf{2}}\mathbf{=}\frac{\mathbf{3}\mathbf{y}^{\mathbf{2}}}{\mathbf{2}}\mathbf{+ c}$ if c is positive ⇒ e = $\sqrt{\frac{5}{3}}$ if c is negative

⇒ e = $\sqrt{\frac{5}{2}}$.