Mathematics
Grade 11
15 min
Convert equations of hyperbolas from general to standard form
Convert equations of hyperbolas from general to standard form
What you'll learn
- Identify the subtraction rule used in an input/output table with four-digit numbers with 80% accuracy.
- Solve subtraction problems with four or more digits to complete input/output tables with 75% accuracy.
- Explain in writing the steps they used to find the missing numbers in a subtraction input/output table, using at least two complete sentences.
- Apply the subtraction rule to generate at least three new output numbers for a given input/output table with four-digit numbers.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the general form of a hyperbola's equation.
Correctly group variable terms and move the constant term in a general equation.
Apply the 'completing the square' method to both the x and y variable groups.
Factor the resulting perfect square trinomials accurately.
Manipulate the equation to set it equal to 1, resulting in the standard form.
Convert a hyperbola's equation from general form to standard form to identify its center and orientation.
Distinguish between the equations for a horizontal and a vertical hyperbola.
How can a messy equation like 4x² - 9y² - 16x + 18y - 29 = 0 possibly describe the elegant, curved path of a comet? ☄️ Let's find out!
This tutorial will guide you through the algebraic process of transfor...
2
Key Concepts & Vocabulary
TermDefinitionExample
General Form of a HyperbolaAn equation of the form Ax² + Cy² + Dx + Ey + F = 0, where A and C have opposite signs (one is positive, one is negative). This form hides the hyperbola's properties.9x² - 16y² - 36x - 32y - 124 = 0
Standard Form of a HyperbolaThe form of a hyperbola's equation that clearly reveals its center (h, k) and orientation. There are two types: one for horizontal and one for vertical hyperbolas.Horizontal: (x-2)²/16 - (y+1)²/9 = 1. Vertical: (y+1)²/9 - (x-2)²/16 = 1.
Completing the SquareAn algebraic technique used to convert a binomial of the form x² + bx into a perfect square trinomial by adding (b/2)². This is the core process for converting from general to standard form.To complete the square for x² + 6x, we add (6/2)² = 3² = 9. This...
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Core Formulas
Standard Form (Horizontal Transverse Axis)
\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1
Use this form when the hyperbola opens left and right. The x-term is positive. The center is (h, k).
Standard Form (Vertical Transverse Axis)
\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1
Use this form when the hyperbola opens up and down. The y-term is positive. The center is (h, k).
4 more steps in this tutorial
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Easy
Which of the following equations is in the general form of a hyperbola as described in the tutorial?
A.(x-1)²/4 - (y+2)²/9 = 1
B.4x² + 9y² - 8x + 36y + 4 = 0
C.5x² - 3y² + 10x - 12y - 22 = 0
D.y = 2(x-3)² + 5
Easy
According to the step-by-step examples, what is the very first step when converting a hyperbola's equation from general to standard form?
A.Group the x-terms and y-terms, and move the constant to the right side.
B.Complete the square for both the x and y variable groups.
C.Factor out the leading coefficients from the variable groups.
D.Divide the entire equation by the constant term.
Easy
What value must be added to the expression x² - 8x to complete the square?
A.-4
B.16
C.8
D.64
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Convert equations of hyperbolas from general to standard form is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Convert equations of hyperbolas from general to standard form?
You'll be able to: Identify the subtraction rule used in an input/output table with four-digit numbers with 80% accuracy; Solve subtraction problems with four or more digits to complete input/output tables with 75% accuracy; Explain in writing the….
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How many practice questions are included with Convert equations of hyperbolas from general to standard form?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.