Question

A standard hyperbola is given as below. Which among the points given would lie on the auxiliary circle of the hyperbola?

• A. A
• B. B
• C. O
• D.

Answer 1

The correct option is A

A

Auxiliary circle is a circle centered at the centre of the hyperbola and passes through the vertices as below.

The equation of the auxiliary circle is given by $x^2+y^2=a^2$, since the radius is 'a' units. And the point A(a,0) certainly satisfies if we substitute in the equation of the auxiliary circle while none of the other points satisfy the equation