Question

Which of the following is/are true for auxilliary circle of rectangular hyperbola
$xy=c^2$

• A. Radius $=\sqrt{2}c$
• B. Diameter $=2\sqrt{2}c$
• C. $x^2+y^2=\sqrt{2}{c}^2$
• D. $x^2+y^2=2c^2$

Answer 1

Answer: (A), (B), (D)

$x^2+y^2=2c^2$

The Auxiliary circle of a rectangular hyperbola is defined as the circle with the center same as the rectangular hyperbola and with transverse axis as it's diameter.

• Diameter $=2\sqrt{2}c$
• Radius $=\sqrt{2}c$
• $x^2+y^2=(\sqrt{2}c{)}^2=2c^2$

Hence, the correct answer are option a, b, c.