Mathematics
Grade 11
15 min
Find the vertices of a hyperbola
Find the vertices of a hyperbola
What you'll learn
- Identify the subtraction rule (the 'minus number') in an input/output table with numbers up to 999.
- Solve for the missing output number in an input/output table by subtracting the rule (the 'minus number') from the input number, with numbers up to 999, with 80% accuracy.
- Apply the subtraction rule to complete an input/output table with at least 3 new inputs and outputs, demonstrating understanding of the pattern.
- Apply the subtraction rule to complete an input/output table with at least 3 input numbers and 3 corresponding, calculated output numbers.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the standard form of a hyperbola's equation.
Determine if a hyperbola's transverse axis is horizontal or vertical based on its equation.
Locate the center (h, k) of a hyperbola from its standard form equation.
Calculate the value of 'a', the distance from the center to a vertex.
Apply the correct formula to find the coordinates of the vertices for both horizontal and vertical hyperbolas.
Distinguish between the vertices and co-vertices of a hyperbola.
Ever wondered how the powerful shape of a nuclear cooling tower is designed or how astronomers map the path of a comet slingshotting around the sun? ☄️ The key points on those hyperbolic curves are the vertices!
This tutorial focuses exclusively on one of the most fundamental sk...
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Key Concepts & Vocabulary
TermDefinitionExample
HyperbolaA type of conic section formed by the intersection of a double cone with a plane. It consists of two separate, mirror-image branches.The equation \frac{x^2}{9} - \frac{y^2}{4} = 1 represents a hyperbola centered at the origin.
Center (h, k)The midpoint of the line segment connecting the two vertices. It is the point of symmetry for the hyperbola.In the hyperbola \frac{(x-2)^2}{16} - \frac{(y+5)^2}{9} = 1, the center is at (2, -5).
Transverse AxisThe line segment that connects the two vertices and passes through the center. Its orientation (horizontal or vertical) determines the direction the hyperbola opens.For a hyperbola opening left and right, the transverse axis is a horizontal line segment.
VerticesThe two points where the hyperbola intersects its trans...
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Core Formulas
Standard Form & Vertices of a Horizontal Hyperbola
Equation: \frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1 \\ Vertices: (h \pm a, k)
Use this when the x-term is positive. The hyperbola opens left and right. To find the vertices, you add and subtract 'a' from the x-coordinate of the center.
Standard Form & Vertices of a Vertical Hyperbola
Equation: \frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1 \\ Vertices: (h, k \pm a)
Use this when the y-term is positive. The hyperbola opens up and down. To find the vertices, you add and subtract 'a' from the y-coordinate of the center.
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Challenging
The vertices of a hyperbola are at (3, 8) and (3, -2). Which of the following could be the equation of this hyperbola?
A.\frac{(x-3)^2}{25} - \frac{(y-3)^2}{b^2} = 1
B.\frac{(y-3)^2}{25} - \frac{(x-3)^2}{b^2} = 1
C.\frac{(y-3)^2}{100} - \frac{(x-3)^2}{b^2} = 1
D.\frac{(y+3)^2}{25} - \frac{(x+3)^2}{b^2} = 1
Challenging
The equation of a hyperbola is kx² - 4y² = 16. If one of its vertices is at (2, 0), what is the value of k?
A.1
B.2
C.4
D.16
Challenging
The transverse axis of a hyperbola is vertical. The distance between its vertices is 18 units, and its center is at (-2, 5). What are the coordinates of the vertices?
A.(7, 5) and (-11, 5)
B.(-2, 23) and (-2, -13)
C.(16, 5) and (-20, 5)
D.(-2, 14) and (-2, -4)
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Frequently asked questions
What grade level is "Find the vertices of a hyperbola"?
Find the vertices of a hyperbola is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find the vertices of a hyperbola?
You'll be able to: Identify the subtraction rule (the 'minus number') in an input/output table with numbers up to 999; Solve for the missing output number in an input/output table by subtracting the rule (the 'minus number') from the input number….
Is "Find the vertices of a hyperbola" free to practice?
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How many practice questions are included with Find the vertices of a hyperbola?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.