For a standard hyperbola x2a2−y2b2=1
Match the following.
Column 1 Column 2
1.a2>b2 P.Director circle is real
2.a2=b2 Q.Director circle is imaginary
3.a2<b2 R.Centre is the only point from which two perpendicular tangents can be drawn on the
hyperbola
1 - P, 2 - R, 3 - Q
Locus of point intersection of the tangents of hyperbola x2a2−y2b2=1 OR director circle of hyperbola is
x2+y2=a2−b2
We can clearly see that if a2>b2, then radius of the circle will have some finite value.
⇒ the director circle is real.
when a2=b2, then radius of the director circle is zero and it reduces to point circle at origin. In this case
centre is the only point from which two perpendicular tangents can be drawn on the curve.
If a2<b2 the radius of the director circle is imaginary, so that there is no such circle and so no pair of
tangents at right angle can be drawn to the hyperbola.