Question

Jeremiah is asked to write the equation of an ellipse. He is given one vertex along the major axis and the location of the center. He realizes he does not have enough information to write the equation. He asks his teacher for one additional piece of information. What information could Jeremiah ask for to help him write the equation? Check all that apply.
-the location of the focus nearest the given vertex
-the location of the focus nearest the other vertex
-the location of the other vertex along the major axis
-the location of one covertex along the minor axis
-the location of the directrix nearest the given vertex
-the location of the directrix nearest the other vertex
-the length of the minor axis

Answer 1

Refer to the figure shown below.

Jeremiah is given the following information:
(i) A vertex along the major axis, located at (a, 0).
(ii) The location of the center which is assumed to be at (0, 0).

The equation for the ellipse is of the form
$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} =1$

If the center of the ellipse is located at (h, k), then the equation is 
$\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} =1$

We know (a), the major axis, but we do not know (b), the minor axis.
We can calculate value for b if we know one focus such as the right focus located at (c, 0), because
c² = a² - b².

Of the choices given, we can gain the required information as follows:
- the location of focus nearest the given vertex (YES)
- the location of the focus nearest the other vertex (YES)
- the location of the other vertex along the major axis (NO)
-  the location of one covertex along the minor axis (YES)
- the location of the directrix nearest the given vertex (NO)
- the location of the directrix nearest the other vertex (NO)
- the length of the minor axis (YES)

Answer 2

The information that could help Jeremiah to write the equations are:

• -the location of the focus nearest the given vertex.
• -the location of the focus nearest the other vertex.

What is an Equation of an Ellipse?

This refers to the plane curve that is between two focal points, in a sense the addition of the two distances to the focal points is a constant.

This equation is written as (x−h)2a2+(y−k)2b2=1.

Where:

• The center is (h,k)
• the larger of a and b is the major radius
• the smaller is the minor radius.

The other answers are:

• -the location of one covertex along the minor axis
• -the location of the directrix nearest the given vertex
• -the location of the directrix nearest the other vertex
• -the length of the minor axis

Read more about equation of an ellipse here:
https://brainly.com/question/16904744