Question

Which of the following describes a conic?

Here S is a fixed point and P is the moving point. 'e' is the eccentricity of the conic

• A. $\frac{PM}{PS}=e$
• B. $\frac{PS}{PM}=e$
• C. $\frac{MS}{PS}=e$
• D. $\frac{PS}{MS}=e$

Answer 1

The correct option is B

$\frac{PS}{PM}=e$

We will derive this from the definition of a conic. A conic section is defined as the locus of a point. The point satisfies the following condition. Its ratio of distance from focus (fixed point) to the perpendicular distance of that point from directrix (fixed line) is constant. That constant is the eccentricity e.

Distance from focus = $PS$

Perpendicular distance from Line = $PM$

Ratio =e $\Rightarrow \frac{PS}{PM}=e$