Mathematics
Grade 10
15 min
Write equations of circles in standard form from graphs
Write equations of circles in standard form from graphs
What you'll learn
- Identify and describe the pattern of adding zeros when multiplying whole numbers by powers of 10 (10, 100, 1000) with at least 80% accuracy on a worksheet.
- Solve multiplication problems involving whole numbers and powers of 10 up to 1,000,000 by 1,000 using mental math strategies and explain their reasoning in writing.
- Apply the understanding of place value patterns to correctly predict the product of a multiplication problem involving large numbers and powers of 10, and verify the answer using a calculator.
- Explain how the number of zeros in a power of 10 relates to the shift in place value when multiplying a whole number by that power of 10, using mathematical vocabulary such as 'ones,' 'tens,' 'hundreds,' and 'thousands'.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Identify the center (h, k) of a circle from its graph.
Determine the radius (r) of a circle by analyzing its graph.
Recall and correctly write the standard form equation of a circle.
Substitute the coordinates of the center (h, k) into the standard form equation, paying close attention to signs.
Substitute the value of the radius (r) into the standard form equation and correctly calculate r-squared.
Write the complete standard form equation for any circle presented graphically.
Ever wondered how your phone's GPS knows your location is within a certain range? 📡 It's all about defining a search area with a circle!
In this tutorial, you will learn the powerful skill of looking at a circle on a graph and writing its specific algebraic equation. Th...
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Key Concepts & Vocabulary
TermDefinitionExample
Coordinate PlaneA two-dimensional plane formed by the intersection of a horizontal line called the x-axis and a vertical line called the y-axis.The grid system you plot points on, like (4, -2).
CircleThe set of all points in a plane that are at a fixed distance from a fixed point.A perfectly round shape like the rim of a wheel.
Center of a CircleThe fixed point from which all points on the circle are equidistant. In the standard equation, it is represented by the coordinates (h, k).If a circle is centered at x=3 and y=5, its center is (3, 5).
RadiusThe fixed distance from the center of the circle to any point on the circle itself. It is represented by the variable 'r'.If the center is at (0,0) and a point on the circle is (0,4), the radius is 4 units.
Stand...
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Core Formulas
Standard Form of a Circle's Equation
(x - h)^2 + (y - k)^2 = r^2
This is the fundamental formula for a circle. Use it to write the final equation. (h, k) is the center of the circle, and r is the radius.
Finding the Center (h, k)
Center = (h, k)
To find the center from a graph, locate the exact middle point of the circle. Identify its x-coordinate (h) and y-coordinate (k).
Finding the Radius (r)
r = \text{distance from center to any point on the circle}
From the center (h, k), count the number of units horizontally or vertically to the edge of the circle. This distance is the radius, r.
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Challenging
A graph shows two concentric circles centered at (2, -1). The smaller circle has a radius of 3. The radius of the larger circle is twice the radius of the smaller circle. What is the equation of the larger circle?
A.(x - 2)^2 + (y + 1)^2 = 36
B.(x - 2)^2 + (y + 1)^2 = 18
C.(x + 2)^2 + (y - 1)^2 = 36
D.(x - 2)^2 + (y + 1)^2 = 9
Challenging
A graph shows a circle whose diameter is the line segment connecting P(7, 1) and Q(-1, -5). Which of the following is the equation of the circle?
A.(x - 3)^2 + (y + 2)^2 = 100
B.(x - 3)^2 + (y + 2)^2 = 25
C.(x + 3)^2 + (y - 2)^2 = 25
D.(x - 6)^2 + (y + 6)^2 = 50
Challenging
A circle is graphed such that its center is at (-4, 3) and it is tangent to the y-axis. What is the equation of the circle?
A.(x + 4)^2 + (y - 3)^2 = 9
B.(x - 4)^2 + (y + 3)^2 = 16
C.(x + 4)^2 + (y - 3)^2 = 16
D.(x + 4)^2 + (y - 3)^2 = 3
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What grade level is "Write equations of circles in standard form from graphs"?
Write equations of circles in standard form from graphs is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Write equations of circles in standard form from graphs?
You'll be able to: Identify and describe the pattern of adding zeros when multiplying whole numbers by powers of 10 (10, 100, 1000) with at least 80% accuracy on a worksheet; Solve multiplication problems involving whole numbers and powers of 10….
Is "Write equations of circles in standard form from graphs" 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 Write equations of circles in standard form from graphs?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.