Question

$(a-3)x^2+a{y}^2=5$ represents a rectangular hyperbola Then the value of $a$ is :

• A. $2$
• B. $1$
• C. $\frac{3}{2}$
• D. $3$

Answer 1

Answer: (C)

$\frac{3}{2}$

The given equation can be written as
$\frac{x^2}{5/a}+\frac{y^2}{5/(a-3)}=1$
If this represents a hyperbola one of $a,a-3is<0$
$\Rightarrow a-3<0$
Hence the equation is $\frac{x^2}{5/a}-\frac{y^2}{5/(3-a)}=\pm 1$
If this represents a rectangular hyperbola $a=3-a$
$\Rightarrow a=\frac{3}{2}$
Hence, option 'C' is correct