Mathematics
Grade 11
15 min
Find the radius or diameter of a circle
Find the radius or diameter of a circle
What you'll learn
- Identify the fraction represented by a shaded area model with up to 8 equal parts with 80% accuracy.
- Divide a given area model (circle, square, rectangle) into a specified number of equal parts (2, 3, 4, 6, or 8) with no more than one visible error per model.
- Explain, using pictures or words, why each part of an area model must be equal in size to represent a fraction correctly.
- Shade a given area model to represent a specific fraction (e.g., shade 2/4 of the circle) with 100% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Find the radius and diameter of a circle given its equation in standard form.
Find the radius and diameter of a circle by converting its equation from general form to standard form using the method of completing the square.
Calculate the radius of a circle using the distance formula when given the coordinates of the center and one point on the circumference.
Determine the radius of a circle by first finding the center and then the length of the radius when given the endpoints of a diameter.
Analyze the value of r^2 to determine if an equation represents a circle, a point (a degenerate circle), or is an impossible case.
Solve applied problems involving the radius or diameter of a circle.
Ever wondered how GPS pinpoints your location using intersecting circ...
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Key Concepts & Vocabulary
TermDefinitionExample
Radius (r)The distance from the center of a circle to any point on its circumference.In a circle with center (0,0) and a point (4,0) on its edge, the radius is 4 units.
Diameter (d)The distance across a circle passing through its center. It is always twice the length of the radius (d = 2r).If a circle's radius is 7 units, its diameter is 14 units.
Center (h, k)The fixed point from which all points on the circle are equidistant.In the equation (x - 2)^2 + (y + 5)^2 = 9, the center is (2, -5).
Standard Equation of a CircleThe form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.(x - 1)^2 + (y - 3)^2 = 16 represents a circle with center (1, 3) and radius 4.
General Equation of a CircleThe form x^2 + y^2 + Dx + Ey + F = 0, which can be co...
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Core Formulas
Radius from Standard Form
(x - h)^2 + (y - k)^2 = r^2
In the standard equation of a circle, the radius 'r' is the principal square root of the constant term on the right side of the equation. Always remember that the equation gives you r², not r.
Finding Radius from General Form
If x^2 + y^2 + Dx + Ey + F = 0, then r^2 = (D/2)^2 + (E/2)^2 - F
To find the radius from the general form, you must first convert it to standard form by completing the square for both x and y terms. The resulting constant on the right side of the equation is r². The radius is then r = √((D/2)² + (E/2)² - F), provided the result is positive.
Radius using the Distance Formula
r = \sqrt{(x_{point} - h)^2 + (y_{point} - k)^2}
When you know the center of the circle (h, k) and any point o...
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Challenging
The equation of a circle is 3x^2 + 3y^2 + 12x - 18y + 39 = 0. What does this equation represent?
A.circle with radius 2
B.An impossible case
C.point
D.circle with radius √39
Challenging
A circle has the general equation x^2 + y^2 - 10x + 4y + c = 0. If the radius of the circle is 7, what is the value of c?
A.-20
B.29
C.20
D.-49
Challenging
Find the radius of a circle with center (5, 3) that is tangent to the line y = -1.
A.5
B.4
C.3
D.6
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What grade level is "Find the radius or diameter of a circle"?
Find the radius or diameter of a circle is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find the radius or diameter of a circle?
You'll be able to: Identify the fraction represented by a shaded area model with up to 8 equal parts with 80% accuracy; Divide a given area model (circle, square, rectangle) into a specified number of equal parts (2, 3, 4, 6, or 8) with no more….
Is "Find the radius or diameter of a circle" free to practice?
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How many practice questions are included with Find the radius or diameter of a circle?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.