Question

The equation,$\frac{x^2}{10-a}+\frac{y^2}{4-a}=1$ represents an ellipse if

• A. $a>4$
• B. $a<4$
• C. $4<a<10$
• D. $a>10$

Answer 1

The correct option is B $a<4$

For the given equation to be an ellipse the only necessary condition is $10-a$ and $4-a$ should be greater than 0.
$\Rightarrow 10-a>0,4-a>0$
$\Rightarrow a<10,a<4$
$\therefore a<4$