Math: Week 2

Welcome back!

DISCLAIMER: All solutions that you will be seeing below might not be necessarily right as I didn’t particularly double-check all of them, yet. With that said, “Yes, I am aware of my answers.” :>

[Not edited nor proofread]

Module 1.2.1

1. Supply the missing steps in the derivation of an equation of the ellipse whose foci are (-c,0) and (c,0) and so that 2a is the constant sum in the definition.

Module 1.2.1: Exercise #1.1

Module 1.2.1: Exercise #1.2

2. What are the coordinates of the farthest points A₁ and A₂ on the ellipse from the center? What are the coordinates of the closest points B₁ and B₂ on the ellipse from the center? To answer these questions, compute the x-intercepts and y-intercepts of

(x²¬a²) + (y²¬b²) = 1

Identify the coordinates of the center, vertices, co-vertices, foci, length of the major axis, and length of the minor axis of the following ellipses:

1. (x²¬36) + (y²¬11) = 1
2. x² = 81–81y²

Module 1.2.1: Exercise #2.1 and #2.2

Module 1.2.2

Exercises 1. Identify the coordinates of the center, vertices, co-vertices, foci, length of the major axis, and length of the minor axis of the ellipse whose equation is given below.

1. (x²¬11) + (y²¬36) = 1
2. 81x² = 81-y²

Module 1.2.2: Exercise #1.1 and #1.2

Exercises 2: Give an equation in the standard form of the horizontal or vertical ellipse described below:

Module 1.2.2: Exercise #2.1

1. The vertical ellipse centered at (-2,-5) whose major axis is 20 units, whose foci are 12 units apart.

Module 1.2.2: Exercise #2.2

2. Center at (3,-2), a vertex at (-12,-2) and a focus at (-6,-2).

Module 1.2.2: Exercise #2.3

3. Vertices at (1,6) and (1,-4) and a co-vertex at (-2,1).

Module 1.2.2: Exercise #2.4

4. Center is (7,4), and (7,8) and (1,4) are two points on the ellipse.

Module 1.2.3

Module 1.2.3: Exercise 1

Exercises 1. Determine the eccentricity of the following and identify which is more circular.

Ellipse 1: [(x+2)²/64] +[(y+5)² /100] = 1

Ellipse 2: 81x² = 81-y²

Exercises 2.

Module 1.2.3: Exercise #2.1a