Question

Which of the following is not true for rectangular hyperbola $xy=4$

• A. Vertices: $(2,2)$ and $(-2,-2)$
• B. Asymptote: $xy=0$
• C. Co-vertices: $(-2,2)$ and $(2,-2)$
• D. Co-vertices: $(-2,-2)$ and $(2,-2)$

Answer 1

The correct option is D Co-vertices: $(-2,-2)$ and $(2,-2)$

Given, Rectangular hyperbola; $xy=4\Rightarrow c=2$
As we know, Vertices of rectangular hyperbola $xy=c^2$ is
$(c,c)$ and $(-c,-c)$
$\to$ Vertices of rectangular hyperbola $xy=4$ is
$(2,2)$ and $(-2,-2)$

$\to$ Co-vertices of rectangular hyperbola $xy=c^2$ is
$(-c,c)$ and $(c,-c)$
$\to$ Co-vertices of rectangular hyperbola $xy=4$ is
$(-2,2)$ and $(2,-2)$

$\to$ Asymptote: $x=0\text{and}y=0\text{or}xy=0$
Hence, the correct answer is Option d.