# What is the Equation of Director Circle of Hyperbola ?

## Solution :

The locus of the intersection of tangents which are at right angles is known as director circle of the hyperbola. The equation to the director circle is :

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

If $$b^2$$ < $$a^2$$, this circle is real ; If $$b^2$$ = $$a^2$$ the radius of the circle is zero & it reduces to a point circle at the origin. In this case the center is the only point from which the tangents at right angles can be drawn to the curve.

If $$b^2$$ > $$a^2$$, the radius of the circle is imaginary, so that there is no such circle & so no tangents at right angle can be drawn to the curve.