Question

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

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

Answer 1

The correct option is A

$a<4$

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