Question

A _______ is the set of points P in the plane such that the ratio of the distance from a fixed point called the ________ to P to the distance from a fixed line called the ______ to the point P equals a constant$e$.

Short answer

A Conic is the set of points P in the plane such that the ratio of the distance from a fixed point called the focus to P to the distance from a fixed line called the directrix to the point P equals a constant

Step-by-step solution

Step 1. Given information

There is a set of points P and a ratio of two distances.

$e$is eccentricity.

Step 2. Identify blank spaces

Since the set of points, P can be on any conic section

So, the first blank should be Conic

We know that

$e=\frac{d(F,P)}{d(D,P)}$

where

d(F,P) means distance from a fixed point (F)focus to P.

d(D,P) means distance from a fixed line (D, directrix) to P.

So,

The second blank is focus

The third blank is directrix