If c is real number and x2c−12+y27−c=1 represents a hyperbola, then

x2c−12+y27−c=1 represents a hyperbola ⇒(c−12>0,7−c 0,c−12 12,7 12 or c<7

If c is real number and x2c−12+y27−c=1 represents a hyperbola, then

x2c−12+y27−c=1 represents a hyperbola ⇒(c−12>0,7−c 0,c−12 12,7 12 or c<7

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If $c$ is real number and $\frac{x^{2}}{c - 12} + \frac{y^{2}}{7 - c} = 1$ represents a hyperbola, then

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$7 < c < 12$

$c < 7$

$c > 12$

$c < 7 or c > 12$

answer is D.

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Detailed Solution

$\frac{x^{2}}{c - 12} + \frac{y^{2}}{7 - c} = 1 represents a hyperbola \Rightarrow (c - 12 > 0, 7 - c < 0) or (7 - c > 0, c - 12 < 0)$

$\Rightarrow (c > 12, 7 < c) or (c < 7; c < 12) \Rightarrow c > 12 or c < 7$

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If c is real number and x2c−12+y27−c=1 represents a hyperbola, then

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If $c$ is real number and $\frac{x^{2}}{c - 12} + \frac{y^{2}}{7 - c} = 1$ represents a hyperbola, then