Q 4 - Calculus

Question

Complete the definitions in Exercises $3-5$.

Given a fixed line in the plane, called the ________, and a given fixed point called the _______, a parabola is the set of all points in the plane ________. 

Step-by-Step Solution

Answer

The complete definition is as following :-

Given a fixed line in the plane, called the directrix, and a given fixed point called the focus, a parabola is the set of all points in the plane equidistant from directrix and focus of the parabola. 

Step 1. Given Information

We have given the following definition:-

Given a fixed line in the plane, called the ________, and a given fixed point called the _______, a parabola is the set of all points in the plane ________.

Step 2. Complete the definition

The given incomplete definition is as follows:

Given a fixed line in the plane, called the ________, and a given fixed point called the _______, a parabola is the set of all points in the plane ________.

We know that in a conic section the given fixed line is called directrix and a given fixed point is known as focus.Then we have:-

Given a fixed line in the plane, called the directrix, and a given fixed point called the focus, 

Also here the word parabola is used. That is this is the definition of a parabola.

We know that the parabola is defined as a set of all points in a plane equidistant from the directrix and focus of the parabola.

From this information, we can complete the given definition as following:-

 Given a fixed line in the plane, called the directrix, and a given fixed point called the focus, a parabola is the set of all points in the plane equidistant from the directrix and focus of the parabola.