Chapter 10.6, Problem 3AYU

A _______ is the set of points $P$ in a 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 $P$ equals a constant $e$.

To determine

To fill: A____ is the set of points $P$ in a 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 ______equals a constant $e$.

Answer to Problem 3AYU

a. Conic.

b. Focus

c. Directrix

Explanation of Solution

Given:

A____ is the set of points $P$ in a 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 ______equals a constant $e$.

Calculation:

A conic is the set of points $P$ in a plane such that the ratio of the distance from $F$ to $P$ to the distance from $D$ to $P$ equals $e$ where $F$ is the focus, the point and $D$ is the directrix, the fixed line.

That is, a conic is the collection of points $P$ for which

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