Question

The equation $\frac{x^2}{12-k}+\frac{y^2}{8-k}=1$ represents

• A. a hyperbola if $k<8$
• B. an ellipse if $k<8$
• C. a hyperbola if $8<k<12$
• D. None of these

Answer 1

The correct option is A a hyperbola if $k<8$

It represents hyperbola if the equation is in the form $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

$\Rightarrow 12-k>0$

$\Rightarrow k<12$

And;

$\Rightarrow 8-k<0$

$\Rightarrow k<8$

Combining both, we get ;

$k<8$