Mathematics
Grade 11
15 min
Find the center of a hyperbola
Find the center of a hyperbola
What you'll learn
- Solve subtraction problems with up to three-digit numbers using regrouping (borrowing) correctly at least 8 out of 10 times.
- Explain the steps you take to solve a three-digit subtraction problem, including when and why you need to regroup, using drawings or words.
- Identify whether or not regrouping is needed in a three-digit subtraction problem with 90% accuracy.
- Apply the concept of subtraction to solve word problems involving three-digit numbers with at least 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the center (h, k) of a hyperbola from its standard form equation.
Distinguish between the standard forms for horizontal and vertical hyperbolas.
Rewrite the general form of a hyperbola's equation into standard form by completing the square.
Accurately extract the values of h and k from any hyperbola equation to locate its center.
Explain the role of the center as the point of intersection for the hyperbola's axes of symmetry.
Solve problems where the center must be found from a non-standard equation form.
How do we pinpoint the source of an earthquake or a thunderclap? 🌩️ The math involves hyperbolas, and finding their center is the critical first step!
This tutorial focuses on one essential skill: finding the center of a hyperbola. Th...
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Key Concepts & Vocabulary
TermDefinitionExample
HyperbolaA type of smooth curve lying in a plane, defined by its geometric properties or by an equation for which it is the solution set. It consists of two separate, mirror-image branches.The equation 9x² - 16y² = 144 describes a hyperbola.
Center (h, k)The midpoint of the line segment connecting the two foci of the hyperbola. It is also the point where the two axes of symmetry, the transverse axis and the conjugate axis, intersect.For the hyperbola (x-2)²/9 - (y-3)²/4 = 1, the center is at the point (2, 3).
Standard Form (Horizontal Transverse Axis)The equation form where the x-term is positive, indicating the hyperbola opens left and right.(x-h)²/a² - (y-k)²/b² = 1
Standard Form (Vertical Transverse Axis)The equation form where the y-term is positive, indicating t...
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Core Formulas
Center from Standard Form (Horizontal)
\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1
When the equation is in this form, the center of the hyperbola is located at the point (h, k). The value 'h' is subtracted from 'x' and the value 'k' is subtracted from 'y'.
Center from Standard Form (Vertical)
\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1
Even when the y-term comes first, the center is still located at (h, k). Be careful to always associate 'h' with the x-variable and 'k' with the y-variable.
4 more steps in this tutorial
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Challenging
The asymptotes of a hyperbola are given by the equations y - 2 = (3/2)(x - 1) and y - 2 = -(3/2)(x - 1). What is the center of the hyperbola?
A.(2, 1)
B.(-1, -2)
C.(1, 2)
D.(3, 2)
Challenging
Find the center of the hyperbola with the equation \frac{(2x + 6)^2}{49} - \frac{(3y - 12)^2}{100} = 1.
A.(-3, 4)
B.(3, -4)
C.(6, -12)
D.(-6, 12)
Challenging
The equation 4x² - 9y² + 8x + 36y + C = 0 represents a hyperbola. What are the coordinates of its center?
A.The center depends on the value of C.
B.(1, -2)
C.(-1, 2)
D.(2, -1)
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Frequently asked questions
What grade level is "Find the center of a hyperbola"?
Find the center of a hyperbola is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find the center of a hyperbola?
You'll be able to: Solve subtraction problems with up to three-digit numbers using regrouping (borrowing) correctly at least 8 out of 10 times; Explain the steps you take to solve a three-digit subtraction problem, including when and why you need….
Is "Find the center of a hyperbola" 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 center of a hyperbola?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.