Question

The equation $\frac{x^2}{14-a}+\frac{y^2}{9-a}=1$ represents a/an

• A. ellipse if $a>9$
• B. hyperbola if $9<a<14$
• C. hyperbola if $a>14$
• D. ellipse if $9<a<14$

Answer 1

Answer: (B)

Given, $\frac{x^2}{14-a}+\frac{y^2}{9-a}=1$
The equation will represent an ellipse if $14-a>0$ and $9-a>0$
$\Rightarrow a<14$ and $a<9$
$\Rightarrow a<9$
a hyperbola if $14-a>0$ and $9-a<0$
$\Rightarrow a<14$ and $a>9$
$\Rightarrow 9<a<14$