Question

If $(\alpha -2)x^2+\alpha y^2=4$ represents a rectangular hyperbola , then $\alpha$ equals to

• A. $0$
• B. $2$
• C. $1$
• D. $3$

Answer 1

The correct option is C $1$

Given,

$(\alpha -2)x^2+\alpha y^2=4$

upon simplification, we get,

$\frac{x^2}{\frac{4}{\alpha -2}}-\frac{y^2}{(-\frac{4}{\alpha })}=1$

Now,

$a^2=\frac{4}{\alpha -2},b^2=-\frac{4}{\alpha }$

for rectangular hyperbola, $a=b$

$\Rightarrow a^2=b^2$

$\frac{4}{\alpha -2}=-\frac{4}{\alpha }$

$-(\alpha -2)=\alpha$

$\therefore \alpha =1$