Mathematics
Grade 11
15 min
Find the length of the major or minor axes of an ellipse
Find the length of the major or minor axes of an ellipse
What you'll learn
- Identify the ordinal number (1st to 100th) when given a position in a sequence, and write it correctly with at least 80% accuracy.
- Explain the difference between a cardinal number (like 1, 2, 3) and an ordinal number (like 1st, 2nd, 3rd) using at least two examples of each.
- Apply ordinal numbers to solve simple word problems involving position, such as 'What is the tenth letter in the word MATHEMATICS?' with 100% accuracy.
- Write the ordinal form of any number between 1 and 100 (e.g., 21st, 43rd, 99th) correctly in at least 4 out of 5 attempts.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the standard form of an ellipse equation, whether centered at the origin or at (h, k).
Determine if an ellipse has a horizontal or vertical orientation based on its equation.
Accurately extract the values of a² and b² from the standard equation of an ellipse.
Calculate the values of 'a' (the semi-major axis) and 'b' (the semi-minor axis).
Apply the formula 2a to find the length of the major axis.
Apply the formula 2b to find the length of the minor axis.
Solve problems where the ellipse equation must first be converted into standard form.
Ever wondered about the shape of a planet's orbit or the design of a 'whispering gallery'? They're ellipses! Let's explore their key dimensions. 🪐
This tutorial w...
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Key Concepts & Vocabulary
TermDefinitionExample
EllipseA set of all points in a plane where the sum of the distances from two fixed points, called the foci, is constant. Visually, it looks like a stretched or flattened circle.The equation \(\frac{x^2}{9} + \frac{y^2}{4} = 1\) describes an ellipse centered at the origin.
Major AxisThe longest diameter of an ellipse. It passes through the center and the two vertices. Its length is always 2a.For an ellipse that is wider than it is tall, the major axis is the horizontal line segment connecting its leftmost and rightmost points.
Minor AxisThe shortest diameter of an ellipse. It passes through the center and the two co-vertices, and is perpendicular to the major axis. Its length is always 2b.For an ellipse that is wider than it is tall, the minor axis is the vertical li...
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Core Formulas
Standard Equation of a Horizontal Ellipse
\(\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\), where \(a > b > 0\)
Use this form when the ellipse is wider than it is tall. The larger denominator, a², is under the x-term. The center is at (h, k).
Standard Equation of a Vertical Ellipse
\(\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1\), where \(a > b > 0\)
Use this form when the ellipse is taller than it is wide. The larger denominator, a², is under the y-term. The center is at (h, k).
Formulas for Axis Lengths
Length of Major Axis = \(2a\) and Length of Minor Axis = \(2b\)
After identifying 'a' (from \(\sqrt{larger \, denominator}\)) and 'b' (from \(\sqrt{smaller \, denominator}\)), use these formulas to find the full lengths of the axes....
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Challenging
Find the length of the minor axis of the ellipse defined by \(5x^2 + 3y^2 + 20x - 18y + 32 = 0\).
A.2√3
B.2√5
C.10
D.6
Challenging
The ellipse \(\frac{x^2}{k+1} + \frac{y^2}{4k-11} = 1\) has a vertical major axis of length 10. What is the length of the minor axis?
A.√10
B.2√10
C.√5
D.2√5
Challenging
What is the length of the major axis for the ellipse defined by the equation \(9(x+1)^2 + 4(y-3)^2 = 1\)?
A.1
B.2/3
C.1/2
D.1/3
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Frequently asked questions
What grade level is "Find the length of the major or minor axes of an ellipse"?
Find the length of the major or minor axes of an ellipse is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find the length of the major or minor axes of an ellipse?
You'll be able to: Identify the ordinal number (1st to 100th) when given a position in a sequence, and write it correctly with at least 80% accuracy; Explain the difference between a cardinal number (like 1, 2, 3) and an ordinal number (like 1st….
Is "Find the length of the major or minor axes of an ellipse" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Find the length of the major or minor axes of an ellipse?
This lesson includes 46 practice questions across multiple difficulty levels, each with instant feedback and explanations.