Question

The intersection point of,a perpendicular on tangent of a hyperbola from the focus and a tangent lies on

• A. director circle
• B. auxillary circle
• C. nine point circle
• D. none

Answer 1

Answer: (B)

auxillary circle

The intersection point of a perpendicular on tangent of a hyperbola from the focus and a tangent lies on: Auxiliary circle

Auxiliary circle of a hyperbola which is a circle described on the major axis of a hyperbola as its diameter.

Let the hyperbola be

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

The equation of auxiliary circle is $x^2+y^2=a^2$

Take a point $P(x_1,y_1)$

Through $P$ draw a line perpendicular to major axis intersecting major axis in $N$ and auxiliary circle in $P^{\prime }$.

The points $P$ and $P^{\prime }$ are called as corresponding points on the hyperbola and auxiliary circle respectively.

This angle is known as the eccentric angle of the point $P$ on the hyperbola and auxiliary circle respectively.