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Q.
The equation $\frac{x^{2}}{14-a}+\frac{y^{2}}{9-a}=1$ represents a/an
Conic Sections
Solution:
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 $a >\, 9$
$\Rightarrow \, 9 < \,a <\, 14$