Chapter 10.2, Problem 6AYU

$\text{A}\left(\text{n}\right)$ _________ is the collection of all points in a plane that are same distance from a fixed point as they are from a fixed line. The line through the focus and perpendicular to the directrix is called the __________ of the parabola.

To determine

To fill: The blanks for the statement, “A(n) _________ is the collection of all points in a plane that are the same distance from a fixed point as they are from a fixed line. The line through the focus and perpendicular to the directrix is called the _________ of the parabola”.

Answer to Problem 6AYU

Solution:

A parabola is the collection of all points in a plane that are the same distance from a fixed point as they are from a fixed line. The line through the focus and perpendicular to the directrix is called the axis of symmetry of the parabola.

Explanation of Solution

Given information:

The statement is, “A(n) __________ is the collection of all points in a plane that are the same distance from a fixed point as they are from a fixed line. The line through the focus and perpendicular to the directrix is called the ________ of the parabola”.

Explanation:

A parabola is the collection of all points that are equidistant from a fixed point and from a fixed line.

The axis of symmetry divides the parabola into two congruent halves.

It always passes through vertex and focus and hence perpendicular to the directrix.

Thus aparabola is the collection of all points in a plane that are the same distance from a fixed point as they are from a fixed line. The line through the focus and perpendicular to the directrix is called the axis of symmetry of the parabola.