Question

If $(a-2)x^2+a{y}^2=4$ represents rectangular hyperbola, then $a$ equals

• A. $0$
• B. $2$
• C. $1$
• D. $3$

Answer 1

Answer: (A)

$0$

Given: Rectangular Hyperbola:$(a-2)x^2+a{y}^2=4$-----------1

We know that for Rectangular Hyperbola, $b^{{}^{\prime }}=a^{{}^{\prime }}$(the general form)

$\Rightarrow$ On simplifying Equation 1, $\frac{x^2}{\frac{4}{a-2}}-\frac{y^2}{\left(\frac{-4}{a}\right)}=1$

where we see , $a^2=\frac{4}{a-2}$ and $b^2=\frac{-4}{a}$

If $b^{{}^{\prime }}=a^{{}^{\prime }}$ $\Rightarrow b^{{}^{\prime }2}=a^{{}^{\prime }2}$

$\Rightarrow \frac{-4}{a}=\frac{4}{a-2}$

$\Rightarrow -(a-2)=a$

$\Rightarrow 2=2a$

$\Rightarrow a=1$