Mathematics
Grade 11
15 min
Find the focus or directrix of a parabola
Find the focus or directrix of a parabola
What you'll learn
- Solve word problems involving finding a unit fraction of a whole number (e.g., 1/2 of 8) with at least 80% accuracy.
- Explain, using pictures or words, how to find a unit fraction of a number in at least 2 out of 3 word problems.
- Identify the unit fraction and the whole number within a word problem with 100% accuracy.
- Apply the strategy of dividing the whole number by the denominator of the unit fraction to solve word problems involving finding a unit fraction of a number.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Define the focus, directrix, vertex, and focal length (p) of a parabola.
Identify the orientation (up, down, left, or right) of a parabola from its standard equation.
Calculate the value of 'p' from the standard equation of a parabola.
Determine the coordinates of the focus for a parabola with its vertex at the origin (0, 0).
Write the equation of the directrix for a parabola with its vertex at the origin (0, 0).
Calculate the coordinates of the focus for a parabola with a translated vertex at (h, k).
Determine the equation of the directrix for a parabola with a translated vertex at (h, k).
Ever wonder how a satellite dish focuses signals onto a single receiver? 📡 That's the magic of a parabola's focus point in action!
This tutoria...
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Key Concepts & Vocabulary
TermDefinitionExample
ParabolaA set of all points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).The graph of the equation y = x² is a parabola.
FocusThe fixed point from which all points on the parabola are equidistant. The parabola always curves around the focus.For the parabola x² = 8y, the focus is located at the point (0, 2).
DirectrixThe fixed line from which all points on the parabola are equidistant. The parabola always curves away from the directrix.For the parabola x² = 8y, the directrix is the horizontal line y = -2.
VertexThe turning point of the parabola. It is the midpoint on the axis of symmetry between the focus and the directrix.For the parabola (x - 3)² = 4(y + 1), the vertex is at the point (3, -1).
Focal Length (p)The di...
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Core Formulas
Standard Equations for a Parabola with Vertex at (0, 0)
Vertical: x² = 4py | Horizontal: y² = 4px
Use these forms when the vertex is at the origin. If x is squared, the parabola is vertical (opens up for p > 0, down for p < 0). If y is squared, it is horizontal (opens right for p > 0, left for p < 0). The focus is at (0, p) for vertical and (p, 0) for horizontal. The directrix is y = -p for vertical and x = -p for horizontal.
Standard Equations for a Parabola with Vertex at (h, k)
Vertical: (x - h)² = 4p(y - k) | Horizontal: (y - k)² = 4p(x - h)
Use these forms for any parabola. The vertex is (h, k). For a vertical parabola, the focus is at (h, k + p) and the directrix is y = k - p. For a horizontal parabola, the focus is at (h + p, k) and the directrix is x = h...
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Challenging
Find the coordinates of the focus of the parabola given by the equation x² + 8x - 8y + 40 = 0.
A.(-4, 5)
B.(-4, 1)
C.(-6, 3)
D.(-2, 3)
Challenging
Find the equation of the directrix of the parabola given by y² - 12y + 20x + 76 = 0.
A.x = 3
B.y = 11
C.x = -3
D.x = 7
Challenging
The focus of a vertical parabola is at (-3, 5) and its vertex is at (-3, 2). What is the equation of its directrix?
A.y = 8
B.y = -1
C.x = 0
D.x = -6
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Frequently asked questions
What grade level is "Find the focus or directrix of a parabola"?
Find the focus or directrix of a parabola is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find the focus or directrix of a parabola?
You'll be able to: Solve word problems involving finding a unit fraction of a whole number (e.g., 1/2 of 8) with at least 80% accuracy; Explain, using pictures or words, how to find a unit fraction of a number in at least 2 out of 3 word problems….
Is "Find the focus or directrix of a parabola" 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 focus or directrix of a parabola?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.