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. None of these

Answer 1

The correct option is D None of these

$\frac{x^2}{10-a}+\frac{y^2}{4-a}=1$

For this equation to represent an ellipse its eccentricity shoule lie between $0$ and $1$.

$\sqrt{1-\frac{b^2}{a^2}}<1$

$0<1-\frac{(4-a{)}^2}{(10-a{)}^2}<1$

$0<(10-a{)}^2-(4-a{)}^2<1$

$0<84-12a<1$

$0<(7-a)12<1$

$12(7-a)>0$ and

$12(7-a)<1$

$a<7$ and $7-a<\frac{1}{12}$

$a<7$ and $a>\frac{83}{12}$