**THE AUXILIARY CIRCLE**

**WHAT IS THE AUXILIARY CIRCLE?**

**The auxiliary circle is the name given to the circle with
its centre on the axis, which contains the two vertices. **

**Figure 2 shows the auxiliary circle for a parabola. **

**Figure 3 shows the auxiliary circle for a hyperbola.**

**COMMON PROPERTY**

**PRINCIPLE:**

*A
perpendicular to a tangent from a focal point will meet the tangent on the
auxiliary circle.*

**THE
ELLIPSE**

**If a line is drawn
from the foci of an ellipse, perpendicular to a tangent it will meet the tangent
on the auxiliary circle.**

**THE PARABOLA**

**If
a line is drawn from the focus of a parabola, perpendicular to any tangent to
the curve, it will meet the tangent on the auxiliary circle. (a tangent at the
vertex)**

**THE HYPERBOLA**

**If
a line is drawn from the foci of a hyperbola, perpendicular to any tangent to
the curve, it will meet the tangent on the auxiliary circle.**