Mathematics
Grade 11
15 min
Find the foci of an ellipse
Find the foci of an ellipse
What you'll learn
- Identify the values of Roman numerals I, V, X, L, C, D, and M with 100% accuracy.
- Translate at least 8 out of 10 Roman numerals (I, V, X, L, C, D, M) into their corresponding Arabic numbers (1, 5, 10, 50, 100, 500, 1000).
- Write at least 3 out of 5 Arabic numbers (between 1 and 39) as Roman numerals using I, V, and X correctly.
- Apply their knowledge of Roman numerals I, V, and X to convert numbers 1-20 from standard form to Roman numeral form with 75% accuracy on an independent practice activity.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the center, major axis, and minor axis of an ellipse from its standard equation.
Determine if an ellipse has a horizontal or vertical orientation.
Calculate the value of 'c', the distance from the center to a focus.
Find the coordinates of the foci for an ellipse centered at the origin (0,0).
Find the coordinates of the foci for an ellipse centered at any point (h, k).
Correctly apply the relationship c^2 = a^2 - b^2 to solve problems.
Ever wondered how a whispering gallery works, where a whisper on one side can be heard clearly across the room? 🤫 The secret lies in the special points of an ellipse called the foci!
This tutorial will guide you through the essential skill of finding the foci of an ellipse. You will learn the key formul...
2
Key Concepts & Vocabulary
TermDefinitionExample
EllipseA flattened circle defined as the set of all points on a plane where the sum of the distances from two fixed points (the foci) is constant.The equation (x^2 / 16) + (y^2 / 9) = 1 describes an ellipse centered at the origin.
Foci (plural of Focus)The two fixed points inside an ellipse that are used to define its shape. They always lie on the major axis.If you tie a string to two pins (the foci) and trace a curve with a pencil held taut against the string, you will draw an ellipse.
Major AxisThe longest diameter of an ellipse, passing through its center and both foci. Its length is 2a.For the ellipse (x^2 / 25) + (y^2 / 16) = 1, the major axis is horizontal and has a length of 2 * sqrt(25) = 10.
Minor AxisThe shortest diameter of an ellipse, passing through the...
3
Core Formulas
Foci Location Formula
c^2 = a^2 - b^2
This is the fundamental formula used to find 'c', the distance from the center to each focus. Remember that 'a^2' is always the larger denominator in the standard equation of an ellipse.
Foci Coordinates for a Horizontal Ellipse
Foci are at (h ± c, k)
Use this when the major axis is horizontal (the larger denominator is under the x-term). You add and subtract 'c' from the x-coordinate of the center (h, k).
Foci Coordinates for a Vertical Ellipse
Foci are at (h, k ± c)
Use this when the major axis is vertical (the larger denominator is under the y-term). You add and subtract 'c' from the y-coordinate of the center (h, k).
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
The foci of an ellipse are at (-1, 3) and (9, 3). The length of the minor axis is 8. Find the value of c, the distance from the center to a focus.
A.c = 4
B.c = 5
C.c = 8
D.c = 10
Challenging
An ellipse has the equation (x^2 / 100) + (y^2 / b^2) = 1, with foci at (±c, 0). What happens to the coordinates of the foci as the value of b^2 approaches 100 (but remains less than 100)?
A.The foci move farther from the center (c increases).
B.The foci do not move (c is constant).
C.The foci move to the y-axis.
D.The foci move closer to the center (c decreases).
Challenging
For an ellipse defined by ((x-h)^2 / p) + ((y-k)^2 / q) = 1, where q > p > 0. Which expression correctly gives the coordinates of the foci?
A.(h ± √(q-p), k)
B.(h, k ± √(q+p))
C.(h, k ± √(q-p))
D.(h ± √(q+p), k)
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing FreeMore from Ellipses
Mathematics for other grades
Frequently asked questions
What grade level is "Find the foci of an ellipse"?
Find the foci of an ellipse is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find the foci of an ellipse?
You'll be able to: Identify the values of Roman numerals I, V, X, L, C, D, and M with 100% accuracy; Translate at least 8 out of 10 Roman numerals (I, V, X, L, C, D, M) into their corresponding Arabic numbers (1, 5, 10, 50, 100, 500, 1000); Write….
Is "Find the foci 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 foci of an ellipse?
This lesson includes 45 practice questions across multiple difficulty levels, each with instant feedback and explanations.