Q 3 - Calculus

Question

Complete the definitions in Exercises $3-5$. 

Given two points in a plane, called _______, an ellipse is the set of points in the plane for which _______.

Step-by-Step Solution

Answer

The complete definition is as following :-

Given two points in a plane, called foci, an ellipse is the set of points in the plane for which the sum of the distances to the two foci is a constant.

Step 1. Given Information

We have given the following definition:-

Given two points in a plane, called _______, an ellipse is the set of points in the plane for which _______.

Step 2. Complete the definition

The given incomplete definition is as follows:-

We know that in a conic section the two fixed points given in a plane are known as foci of the conic section. Then we have :-

Given two points in a plane, called foci, 

Here the word ellipse is used. That is this is the definition of an ellipse.

We know that the ellipse is the set of points in the plane such that the sum of the distances to the two foci is a constant.

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

Given two points in a plane, called foci, an ellipse is the set of points in the plane for which the sum of the distances to the two foci is a constant.