Question

From a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ lines are drawn to focus S

and directrix perpendicular to it as shown.Then,

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

A hyperbola by definition is the locus of a point in a plane which moves in the plne in such a way that the ratio of its distance from a fixed point, focus, in the same plane to its distance from a fixed line, called directrix, is a constant. This constant is always greater than 1, and is called eccentricity-, 'e'

i.e.,$e=\frac{PS}{PD}>1$

i.e.,$PS>PD$.