Mathematics
Grade 11
15 min
Find the equations for the asymptotes of a hyperbola
Find the equations for the asymptotes of a hyperbola
What you'll learn
- Solve subtraction problems with up to three-digit numbers, using strategies like regrouping, with 80% accuracy on a worksheet.
- Explain the steps for subtracting two- and three-digit numbers in their own words to a partner, demonstrating understanding of regrouping when necessary.
- Identify whether regrouping is needed in a three-digit subtraction problem with 100% accuracy.
- Apply subtraction skills to solve real-world word problems involving up to three-digit numbers, showing their work and arriving at the correct answer at least 3 out of 4 times.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define what an asymptote of a hyperbola is and its relationship to the hyperbola's branches.
Identify the center (h, k), and the values of 'a' and 'b' from the standard equation of a hyperbola.
State the formulas for the asymptotes of both horizontal and vertical hyperbolas centered at (h, k).
Derive the equations of the asymptotes for a hyperbola given its standard form equation.
Differentiate between the asymptote equations for a horizontal hyperbola and a vertical hyperbola based on the slope.
Use the center and slopes to accurately describe the lines that guide the hyperbola's graph.
Ever wonder what invisible lines guide the path of a comet as it slingshots around the sun? ☄️ These guiding lines are the asymptotes of a h...
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Key Concepts & Vocabulary
TermDefinitionExample
HyperbolaA conic section consisting of two separate, mirror-image branches. It is defined as the set of all points where the difference of the distances from two fixed points (the foci) is constant.The graph of the equation `x^2/9 - y^2/4 = 1` is a hyperbola that opens to the left and right.
AsymptoteA line that a curve approaches but never touches as it heads towards infinity. For a hyperbola, the two asymptotes form an 'X' shape that the branches get closer and closer to.For the hyperbola `x^2/9 - y^2/4 = 1`, the lines `y = (2/3)x` and `y = -(2/3)x` are its asymptotes.
Center (h, k)The midpoint between the two vertices of the hyperbola. It is the point where the two asymptotes intersect.In the equation `(x-1)^2/16 - (y+2)^2/9 = 1`, the center is at the po...
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Core Formulas
Asymptote Equations for a Horizontal Hyperbola
For `(x-h)^2/a^2 - (y-k)^2/b^2 = 1`, the asymptotes are `y - k = ±(b/a)(x - h)`.
Use this formula when the x-term is positive, meaning the hyperbola opens left and right. The slope of the asymptotes is `±(b/a)`, which can be remembered as `±(y-radius / x-radius)` of the central box.
Asymptote Equations for a Vertical Hyperbola
For `(y-k)^2/a^2 - (x-h)^2/b^2 = 1`, the asymptotes are `y - k = ±(a/b)(x - h)`.
Use this formula when the y-term is positive, meaning the hyperbola opens up and down. The slope of the asymptotes is `±(a/b)`. Note the change in the slope formula compared to the horizontal case.
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Challenging
Find the equations of the asymptotes for the hyperbola defined by 9x^2 - 4y^2 - 72x + 8y + 176 = 0.
A.y - 1 = ±(3/2)(x - 4)
B.y - 4 = ±(3/2)(x - 1)
C.y - 1 = ±(2/3)(x - 4)
D.y - 4 = ±(2/3)(x - 1)
Challenging
A hyperbola has vertices at (0, ±6) and foci at (0, ±10). What are the equations of its asymptotes?
A.y = ±(5/3)x
B.y = ±(3/4)x
C.y = ±(4/3)x
D.y = ±(4/5)x
Challenging
If the value of 'b' in the equation x^2/a^2 - y^2/b^2 = 1 is doubled, how does the slope of the asymptotes change?
A.The slope is halved.
B.The slope is quadrupled.
C.The slope is doubled.
D.The slope does not change.
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Frequently asked questions
What grade level is "Find the equations for the asymptotes of a hyperbola"?
Find the equations for the asymptotes of a hyperbola is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find the equations for the asymptotes of a hyperbola?
You'll be able to: Solve subtraction problems with up to three-digit numbers, using strategies like regrouping, with 80% accuracy on a worksheet; Explain the steps for subtracting two- and three-digit numbers in their own words to a partner….
Is "Find the equations for the asymptotes 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 equations for the asymptotes of a hyperbola?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.