P is a moving point, S is the focus and L is the directrix as shown in figure.

Which of the following represents the equation of a conic?

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Solution

The correct options are
A

B

A conic is the locus of all points whose ratio of distance from focus (PS) is the perpendicular distance

from directrix (PM) is a constant.

$\Rightarrow \frac{P S}{P M} = k$

This constant k is denoted by e ,the eccentricity.But we are not given this in question .so we can write

$\frac{P M}{P S} = \frac{1}{k} = k^{1}$ .we can replace k and $k^{1}$ to get $\frac{P S}{P M} = e a n d \frac{P M}{P S} = e$ .Both can represent a conic.

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