Mathematics
Grade 11
15 min
Find the center, vertices, or co-vertices of an ellipse
Find the center, vertices, or co-vertices of an ellipse
What you'll learn
- Write numbers from 0 to 100 in words correctly with at least 80% accuracy on a worksheet.
- Identify the correct number word representation when given three choices for numbers up to 1000, achieving a score of 7 out of 10 on a quiz.
- Explain the relationship between the digits in a number (ones, tens, hundreds) and how it affects writing the number in words, providing at least two correct examples.
- Correctly write the word form of any number from a given list of ten numbers between 1 and 100.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Identify the center (h, k) of an ellipse from its standard equation.
Determine whether an ellipse has a horizontal or vertical major axis by comparing denominators.
Calculate the values of 'a' (major radius) and 'b' (minor radius) from the equation.
Find the exact coordinates of the vertices.
By the end of a this lesson, students will be able to find the exact coordinates of the co-vertices.
Distinguish between vertices and co-vertices and relate them to the major and minor axes.
Ever wondered about the shape of a planet's orbit or the design of a 'whispering gallery' where a secret can be heard across the room? 🪐 They're all based on the ellipse!
In this tutorial, we will break down the standard equation of an el...
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Key Concepts & Vocabulary
TermDefinitionExample
EllipseA flattened circle; the set of all points in a plane where the sum of the distances from two fixed points (the foci) is constant.The path the Earth takes around the Sun is an ellipse.
Center (h, k)The midpoint of both the major and minor axes. It is the central point from which the ellipse is symmetric.In the ellipse equation (x-3)^2/16 + (y+2)^2/9 = 1, the center is at the point (3, -2).
Major AxisThe longer axis of an ellipse, passing through the center and the two vertices. Its length is 2a.If an ellipse is wider than it is tall, its major axis is horizontal.
VerticesThe endpoints of the major axis. They are the two points on the ellipse that are farthest from the center.For a horizontal ellipse centered at (0,0) with a=5, the vertices are at (5,0) and (-5,...
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Core Formulas
Standard Equation of a Horizontal Ellipse
\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1
Use this form when the ellipse is wider than it is tall. The larger denominator, a^2, is under the x-term. Here, a > b. The center is (h, k), vertices are (h±a, k), and co-vertices are (h, k±b).
Standard Equation of a Vertical Ellipse
\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1
Use this form when the ellipse is taller than it is wide. The larger denominator, a^2, is under the y-term. Here, a > b. The center is (h, k), vertices are (h, k±a), and co-vertices are (h±b, k).
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Challenging
An ellipse has vertices at (-2, 8) and (-2, -4) and co-vertices at (1, 2) and (-5, 2). What is the standard equation of this ellipse?
A.\frac{(x+2)^2}{36} + \frac{(y-2)^2}{9} = 1
B.\frac{(x+2)^2}{9} + \frac{(y-2)^2}{36} = 1
C.\frac{(x-2)^2}{9} + \frac{(y+2)^2}{36} = 1
D.\frac{(x-2)^2}{36} + \frac{(y+2)^2}{9} = 1
Challenging
The center of an ellipse is (5, -3). One vertex is at (5, 2), and the length of the minor axis is 8. What are the coordinates of the co-vertices?
A.(9, -3) and (1, -3)
B.(5, 1) and (5, -7)
C.(13, -3) and (-3, -3)
D.(5, 5) and (5, -11)
Challenging
An ellipse has its center at (-1, 3). One of its co-vertices is at (-1, 7), and its major axis has a length of 10. What are the coordinates of the vertices?
A.(-1, 8) and (-1, -2)
B.(-1, 13) and (-1, -7)
C.(3, 3) and (-5, 3)
D.(4, 3) and (-6, 3)
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Find the center, vertices, or co-vertices of an ellipse is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find the center, vertices, or co-vertices of an ellipse?
You'll be able to: Write numbers from 0 to 100 in words correctly with at least 80% accuracy on a worksheet; Identify the correct number word representation when given three choices for numbers up to 1000, achieving a score of 7 out of 10 on a….
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This lesson includes 44 practice questions across multiple difficulty levels, each with instant feedback and explanations.