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If the equation $(10 x - 5)^{2} + (10 y - 4)^{2} = λ^{2} (3 x + 4 y - 1)^{2}$ represents a hyperbola then

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$- 2 < λ < 2$

$0 < λ < 2$

$λ < - 2, λ > 2$

$λ > 2$

answer is C.

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Detailed Solution

$\begin{array}{l} {(x - \frac{1}{2})}^{2} + {(y - \frac{2}{5})}^{2} = {(\frac{λ}{2})}^{2} {(\frac{3 x + 4 y - 1}{5})}^{2} \\ \Rightarrow SP = |\frac{λ}{2}| PM \Rightarrow \frac{| λ |}{2} > 1 \end{array}$

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