Question

If equation (10x - 5)² + (10y - 4)² = λ²(3x + 4y - 1)² represents a hyperbola then:

• A. -2 <λ< 2
• B. λ> 2
• C. λ< -2 or λ> 2
• D. 0 <λ< 2

Answer 1

Answer: (C)

λ< -2 or λ> 2

Answer 2

$\frac{\sqrt{\left( \mathbf{x}\mathbf{-}\frac{\mathbf{1}}{\mathbf{2}} \right)^{\mathbf{2}}\mathbf{+}\left( \mathbf{y}\mathbf{-}\frac{\mathbf{2}}{\mathbf{5}} \right)^{\mathbf{2}}}}{\left| \frac{\mathbf{3x + 4y}\mathbf{-}\mathbf{1}}{\mathbf{5}} \right|}\mathbf{=}\left| \frac{\mathbf{\lambda}}{\mathbf{2}} \right|$,

Here $\left| \frac{\lambda}{2} \right| > 1 \Rightarrow |\lambda| > 2$

⇒ λ < -2 or λ > 2.