Question

The equation of director circle of $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is:

• A. Imaginary if $a<b$
• B. Imaginary if $a>b$
• C. Point circle if $a=b$
• D. None of the above

Answer 1

Answer: (A), (C)

The correct options are
A Imaginary if $a<b$
C Point circle if $a=b$

The director circle of an hyperbola circumscribes the minimum bounding box of the hyperbola.it has the same center as the hyperbola, with radius $\sqrt{a^2-b^2}$ where $a$ and $b$ are the semi-major axis and semi-minor axis of the hyperbola.

equation of circle is

$x^2+y^2=a^2-b^2$

$a<b$ then circle radius is negative and circle is imaginary

$a=b$ then circle radius is zero and circle is point circle